diff --git a/cranelift/codegen/src/opts/icmp.isle b/cranelift/codegen/src/opts/icmp.isle
index 024e6668f02a..abb7a61576a0 100644
--- a/cranelift/codegen/src/opts/icmp.isle
+++ b/cranelift/codegen/src/opts/icmp.isle
@@ -15,14 +15,14 @@
 
 ;; Optimize icmp-of-icmp.
 ;; ne(icmp(ty, cc, x, y), 0) == icmp(ty, cc, x, y)
-;; e.g. neq(ugt(x, y), 0) == ugt(x, y) 
+;; e.g. neq(ugt(x, y), 0) == ugt(x, y)
 (rule (simplify (ne ty
                       (uextend_maybe _ inner @ (icmp ty _ _ _))
                       (iconst_u _ 0)))
       (subsume inner))
 
 ;; eq(icmp(ty, cc, x, y), 0) == icmp(ty, cc_complement, x, y)
-;; e.g. eq(ugt(x, y), 0) == ule(x, y) 
+;; e.g. eq(ugt(x, y), 0) == ule(x, y)
 (rule (simplify (eq ty
                       (uextend_maybe _ (icmp ty cc x y))
                       (iconst_u _ 0)))
@@ -65,11 +65,37 @@
              (iconst_u _ 1)))
       extend)
 
+;; Rewrite loose inequalities to strict inequalities:
+;; ule(x, c) == ult(x, c+1), for c != UMAX.
+(rule (simplify (ule (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 c))))
+      (if-let $false (u64_eq c (ty_umax cty)))
+      (ult bty x (iconst cty (imm64 (u64_add c 1)))))
+
+;; uge(x, c) == ugt(x, c-1), for c != 0.
+(rule (simplify (uge (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 c))))
+      (if-let $false (u64_eq c 0))
+      (ugt bty x (iconst cty (imm64 (u64_sub c 1)))))
+
+;; sle(x, c) == slt(x, c+1), for c != SMAX.
+(rule (simplify (sle (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 c))))
+      (if-let $false (u64_eq c (ty_smax cty)))
+      (slt bty x (iconst cty (imm64 (u64_add c 1)))))
+
+;; FIXME: triggers verifier error
+;; sge(x, c) == sgt(x, c-1), for c != SMIN.
+;; (rule (simplify (sge (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 c))))
+;;      (if-let $false (u64_eq c (ty_smin cty)))
+;;      (sgt bty x (iconst cty (imm64 (u64_sub c 1)))))
+
 ;; Comparisons against largest/smallest signed/unsigned values:
 ;; ult(x, 0) == false.
 (rule (simplify (ult (fits_in_64 (ty_int bty)) x zero @ (iconst_u _ 0)))
       (subsume (iconst_u bty 0)))
 
+;; ult(x, 1) == eq(x, 0)
+(rule (simplify (ult (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 0))))
+      (eq bty x (iconst cty (imm64 0))))
+
 ;; ule(x, 0) == eq(x, 0)
 (rule (simplify (ule (fits_in_64 (ty_int bty)) x zero @ (iconst_u _ 0)))
       (eq bty x zero))
@@ -78,6 +104,11 @@
 (rule (simplify (ugt (fits_in_64 (ty_int bty)) x zero @ (iconst_u _ 0)))
       (ne bty x zero))
 
+;; ugt(x, UMAX-1) == eq(x, UMAX).
+(rule (simplify (ugt (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 y))))
+      (if-let $true (u64_eq y (u64_sub (ty_umax cty) 1)))
+      (eq bty x (iconst cty (imm64 (ty_umax cty)))))
+
 ;; uge(x, 0) == true.
 (rule (simplify (uge (fits_in_64 (ty_int bty)) x zero @ (iconst_u _ 0)))
       (subsume (iconst_u bty 1)))
@@ -112,6 +143,11 @@
        (if-let $true (u64_eq y (ty_smin cty)))
        (eq bty x smin))
 
+;; slt(x, SMIN+1) == eq(x, SMIN).
+(rule (simplify (slt (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 y))))
+       (if-let $true (u64_eq y (u64_add (ty_smin cty) 1)))
+       (eq bty x (iconst cty (imm64 (ty_smin cty)))))
+
 ;; sgt(x, SMIN) == ne(x, SMIN).
 (rule (simplify (sgt (fits_in_64 (ty_int bty)) x smin @ (iconst_u cty y)))
        (if-let $true (u64_eq y (ty_smin cty)))
@@ -142,6 +178,11 @@
        (if-let $true (u64_eq y (ty_smax cty)))
        (eq bty x smax))
 
+;; sgt(x, SMAX-1) == eq(x, SMAX).
+(rule (simplify (sgt (fits_in_64 (ty_int bty)) x (iconst cty (u64_from_imm64 y))))
+       (if-let $true (u64_eq y (u64_sub (ty_smax cty) 1)))
+       (eq bty x (iconst cty (imm64 (ty_smax cty)))))
+
 ;; `band`/`bor` of 2 comparisons:
 (rule (simplify (band (fits_in_64 ty) (icmp ty cc1 x y) (icmp ty cc2 x y)))
   (if-let signed (intcc_comparable cc1 cc2))
diff --git a/cranelift/filetests/filetests/egraph/cprop.clif b/cranelift/filetests/filetests/egraph/cprop.clif
index f1ca491f4977..f23dde1c63bf 100644
--- a/cranelift/filetests/filetests/egraph/cprop.clif
+++ b/cranelift/filetests/filetests/egraph/cprop.clif
@@ -162,8 +162,8 @@ block0:
     return v2
 }
 
-; check: v3 = iconst.i8 1
-; nextln: return v3
+; check: v5 = iconst.i8 1
+; nextln: return v5
 
 function %icmp_uge_i32() -> i8 {
 block0:
@@ -173,8 +173,8 @@ block0:
     return v2
 }
 
-; check: v3 = iconst.i8 0
-; nextln: return v3
+; check: v4 = iconst.i8 0
+; nextln: return v4
 
 function %icmp_ugt_i32() -> i8 {
 block0:
@@ -206,8 +206,8 @@ block0:
     return v2
 }
 
-; check: v3 = iconst.i8 1
-; nextln: return v3
+; check: v5 = iconst.i8 1
+; nextln: return v5
 
 function %icmp_sge_i32() -> i8 {
 block0:
diff --git a/cranelift/filetests/filetests/egraph/icmp-parameterized.clif b/cranelift/filetests/filetests/egraph/icmp-parameterized.clif
index 0ce76115c611..96c14f2fdf89 100644
--- a/cranelift/filetests/filetests/egraph/icmp-parameterized.clif
+++ b/cranelift/filetests/filetests/egraph/icmp-parameterized.clif
@@ -3,7 +3,7 @@ set opt_level=speed
 target x86_64
 
 ;; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-;; !!! GENERATED BY 'make-parameterized-icmp-tests.sh' DO NOT EDIT !!!
+;; !!! GENERATED BY 'make-icmp-parameterized-tests.sh' DO NOT EDIT !!!
 ;; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 ;; run with the 'CRANELIFT_TEST_BLESS=1' env var set to update this file
 
@@ -127,36 +127,6 @@ block0(v0: i32):
 ;     return v2  ; v2 = 1
 ; }
 
-function %mask_icmp_result(i64, i64) -> i8 {
-block0(v1: i64, v2: i64):
-    v3 = icmp ult v1, v2
-    v4 = iconst.i8 1
-    v5 = band v3, v4
-    return v5
-}
-
-; function %mask_icmp_result(i64, i64) -> i8 fast {
-; block0(v1: i64, v2: i64):
-;     v3 = icmp ult v1, v2
-;     return v3
-; }
-
-function %mask_icmp_extend_result(i64, i64) -> i64 {
-block0(v1: i64, v2: i64):
-    v3 = icmp ult v1, v2
-    v4 = uextend.i64 v3
-    v5 = iconst.i64 1
-    v6 = band v4, v5
-    return v6
-}
-
-; function %mask_icmp_extend_result(i64, i64) -> i64 fast {
-; block0(v1: i64, v2: i64):
-;     v3 = icmp ult v1, v2
-;     v4 = uextend.i64 v3
-;     return v4
-; }
-
 function %icmp_eq_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -171,6 +141,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_eq_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp eq v0, v1
+    return v2
+}
+
+; function %icmp_eq_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 1
+;     v2 = icmp eq v0, v1  ; v1 = 1
+;     return v2
+; }
+
 function %icmp_eq_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -185,6 +169,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_eq_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp eq v0, v1
+    return v2
+}
+
+; function %icmp_eq_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp eq v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_eq_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -199,6 +197,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_eq_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp eq v0, v1
+    return v2
+}
+
+; function %icmp_eq_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp eq v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_eq_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -213,6 +225,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_eq_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp eq v0, v1
+    return v2
+}
+
+; function %icmp_eq_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp eq v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_ne_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -227,6 +253,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ne_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp ne v0, v1
+    return v2
+}
+
+; function %icmp_ne_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 1
+;     v2 = icmp ne v0, v1  ; v1 = 1
+;     return v2
+; }
+
 function %icmp_ne_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -241,6 +281,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ne_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp ne v0, v1
+    return v2
+}
+
+; function %icmp_ne_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp ne v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_ne_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -255,6 +309,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ne_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp ne v0, v1
+    return v2
+}
+
+; function %icmp_ne_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp ne v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_ne_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -269,6 +337,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ne_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp ne v0, v1
+    return v2
+}
+
+; function %icmp_ne_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp ne v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_ult_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -282,6 +364,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 0
 ; }
 
+function %icmp_ult_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp ult v0, v1
+    return v2
+}
+
+; function %icmp_ult_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0
+;     v4 = icmp eq v0, v3  ; v3 = 0
+;     return v4
+; }
+
 function %icmp_ult_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -296,6 +392,20 @@ block0(v0: i32):
 ;     return v3
 ; }
 
+function %icmp_ult_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp ult v0, v1
+    return v2
+}
+
+; function %icmp_ult_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp ult v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_ult_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -310,6 +420,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ult_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp ult v0, v1
+    return v2
+}
+
+; function %icmp_ult_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp ult v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_ult_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -324,6 +448,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ult_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp ult v0, v1
+    return v2
+}
+
+; function %icmp_ult_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp ult v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_ule_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -334,8 +472,22 @@ block0(v0: i32):
 ; function %icmp_ule_umin(i32) -> i8 fast {
 ; block0(v0: i32):
 ;     v1 = iconst.i32 0
-;     v3 = icmp eq v0, v1  ; v1 = 0
-;     return v3
+;     v5 = icmp eq v0, v1  ; v1 = 0
+;     return v5
+; }
+
+function %icmp_ule_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp ule v0, v1
+    return v2
+}
+
+; function %icmp_ule_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 2
+;     v4 = icmp ult v0, v3  ; v3 = 2
+;     return v4
 ; }
 
 function %icmp_ule_umax(i32) -> i8 {
@@ -351,6 +503,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 1
 ; }
 
+function %icmp_ule_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp ule v0, v1
+    return v2
+}
+
+; function %icmp_ule_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0xffff_ffff
+;     v5 = icmp ne v0, v3  ; v3 = 0xffff_ffff
+;     return v5
+; }
+
 function %icmp_ule_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -360,9 +526,23 @@ block0(v0: i32):
 
 ; function %icmp_ule_smin(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v1 = iconst.i32 0x8000_0000
-;     v2 = icmp ule v0, v1  ; v1 = 0x8000_0000
-;     return v2
+;     v3 = iconst.i32 0x8000_0001
+;     v4 = icmp ult v0, v3  ; v3 = 0x8000_0001
+;     return v4
+; }
+
+function %icmp_ule_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp ule v0, v1
+    return v2
+}
+
+; function %icmp_ule_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x8000_0002
+;     v4 = icmp ult v0, v3  ; v3 = 0x8000_0002
+;     return v4
 ; }
 
 function %icmp_ule_smax(i32) -> i8 {
@@ -374,9 +554,23 @@ block0(v0: i32):
 
 ; function %icmp_ule_smax(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v1 = iconst.i32 0x7fff_ffff
-;     v2 = icmp ule v0, v1  ; v1 = 0x7fff_ffff
-;     return v2
+;     v3 = iconst.i32 0x8000_0000
+;     v4 = icmp ult v0, v3  ; v3 = 0x8000_0000
+;     return v4
+; }
+
+function %icmp_ule_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp ule v0, v1
+    return v2
+}
+
+; function %icmp_ule_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x7fff_ffff
+;     v4 = icmp ult v0, v3  ; v3 = 0x7fff_ffff
+;     return v4
 ; }
 
 function %icmp_ugt_umin(i32) -> i8 {
@@ -393,6 +587,20 @@ block0(v0: i32):
 ;     return v3
 ; }
 
+function %icmp_ugt_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp ugt v0, v1
+    return v2
+}
+
+; function %icmp_ugt_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 1
+;     v2 = icmp ugt v0, v1  ; v1 = 1
+;     return v2
+; }
+
 function %icmp_ugt_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -406,6 +614,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 0
 ; }
 
+function %icmp_ugt_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp ugt v0, v1
+    return v2
+}
+
+; function %icmp_ugt_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0xffff_ffff
+;     v4 = icmp eq v0, v3  ; v3 = 0xffff_ffff
+;     return v4
+; }
+
 function %icmp_ugt_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -420,6 +642,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ugt_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp ugt v0, v1
+    return v2
+}
+
+; function %icmp_ugt_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp ugt v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_ugt_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -434,6 +670,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_ugt_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp ugt v0, v1
+    return v2
+}
+
+; function %icmp_ugt_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp ugt v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_uge_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -447,6 +697,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 1
 ; }
 
+function %icmp_uge_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp uge v0, v1
+    return v2
+}
+
+; function %icmp_uge_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0
+;     v5 = icmp ne v0, v3  ; v3 = 0
+;     return v5
+; }
+
 function %icmp_uge_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -456,9 +720,23 @@ block0(v0: i32):
 
 ; function %icmp_uge_umax(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v1 = iconst.i32 0xffff_ffff
-;     v3 = icmp eq v0, v1  ; v1 = 0xffff_ffff
-;     return v3
+;     v4 = iconst.i32 0xffff_fffe
+;     v5 = icmp ugt v0, v4  ; v4 = 0xffff_fffe
+;     return v5
+; }
+
+function %icmp_uge_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp uge v0, v1
+    return v2
+}
+
+; function %icmp_uge_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0xffff_fffd
+;     v4 = icmp ugt v0, v3  ; v3 = 0xffff_fffd
+;     return v4
 ; }
 
 function %icmp_uge_smin(i32) -> i8 {
@@ -470,9 +748,23 @@ block0(v0: i32):
 
 ; function %icmp_uge_smin(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v1 = iconst.i32 0x8000_0000
-;     v2 = icmp uge v0, v1  ; v1 = 0x8000_0000
-;     return v2
+;     v3 = iconst.i32 0x7fff_ffff
+;     v4 = icmp ugt v0, v3  ; v3 = 0x7fff_ffff
+;     return v4
+; }
+
+function %icmp_uge_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp uge v0, v1
+    return v2
+}
+
+; function %icmp_uge_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x8000_0000
+;     v4 = icmp ugt v0, v3  ; v3 = 0x8000_0000
+;     return v4
 ; }
 
 function %icmp_uge_smax(i32) -> i8 {
@@ -484,9 +776,23 @@ block0(v0: i32):
 
 ; function %icmp_uge_smax(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v1 = iconst.i32 0x7fff_ffff
-;     v2 = icmp uge v0, v1  ; v1 = 0x7fff_ffff
-;     return v2
+;     v3 = iconst.i32 0x7fff_fffe
+;     v4 = icmp ugt v0, v3  ; v3 = 0x7fff_fffe
+;     return v4
+; }
+
+function %icmp_uge_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp uge v0, v1
+    return v2
+}
+
+; function %icmp_uge_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x7fff_fffd
+;     v4 = icmp ugt v0, v3  ; v3 = 0x7fff_fffd
+;     return v4
 ; }
 
 function %icmp_slt_umin(i32) -> i8 {
@@ -503,6 +809,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_slt_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp slt v0, v1
+    return v2
+}
+
+; function %icmp_slt_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 1
+;     v9 = icmp slt v0, v1  ; v1 = 1
+;     return v9
+; }
+
 function %icmp_slt_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -517,6 +837,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_slt_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp slt v0, v1
+    return v2
+}
+
+; function %icmp_slt_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp slt v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_slt_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -530,6 +864,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 0
 ; }
 
+function %icmp_slt_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp slt v0, v1
+    return v2
+}
+
+; function %icmp_slt_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x8000_0000
+;     v4 = icmp eq v0, v3  ; v3 = 0x8000_0000
+;     return v4
+; }
+
 function %icmp_slt_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -544,6 +892,20 @@ block0(v0: i32):
 ;     return v3
 ; }
 
+function %icmp_slt_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp slt v0, v1
+    return v2
+}
+
+; function %icmp_slt_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp slt v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_sle_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -554,8 +916,22 @@ block0(v0: i32):
 ; function %icmp_sle_umin(i32) -> i8 fast {
 ; block0(v0: i32):
 ;     v1 = iconst.i32 0
-;     v2 = icmp sle v0, v1  ; v1 = 0
-;     return v2
+;     v9 = icmp sle v0, v1  ; v1 = 0
+;     return v9
+; }
+
+function %icmp_sle_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp sle v0, v1
+    return v2
+}
+
+; function %icmp_sle_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 2
+;     v4 = icmp slt v0, v3  ; v3 = 2
+;     return v4
 ; }
 
 function %icmp_sle_umax(i32) -> i8 {
@@ -567,8 +943,22 @@ block0(v0: i32):
 
 ; function %icmp_sle_umax(i32) -> i8 fast {
 ; block0(v0: i32):
-;     v3 = iconst.i32 0
-;     v4 = icmp slt v0, v3  ; v3 = 0
+;     v5 = iconst.i32 0
+;     v6 = icmp slt v0, v5  ; v5 = 0
+;     return v6
+; }
+
+function %icmp_sle_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp sle v0, v1
+    return v2
+}
+
+; function %icmp_sle_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0xffff_ffff
+;     v4 = icmp slt v0, v3  ; v3 = 0xffff_ffff
 ;     return v4
 ; }
 
@@ -582,8 +972,22 @@ block0(v0: i32):
 ; function %icmp_sle_smin(i32) -> i8 fast {
 ; block0(v0: i32):
 ;     v1 = iconst.i32 0x8000_0000
-;     v3 = icmp eq v0, v1  ; v1 = 0x8000_0000
-;     return v3
+;     v5 = icmp eq v0, v1  ; v1 = 0x8000_0000
+;     return v5
+; }
+
+function %icmp_sle_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp sle v0, v1
+    return v2
+}
+
+; function %icmp_sle_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x8000_0002
+;     v4 = icmp slt v0, v3  ; v3 = 0x8000_0002
+;     return v4
 ; }
 
 function %icmp_sle_smax(i32) -> i8 {
@@ -599,6 +1003,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 1
 ; }
 
+function %icmp_sle_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp sle v0, v1
+    return v2
+}
+
+; function %icmp_sle_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x7fff_ffff
+;     v5 = icmp ne v0, v3  ; v3 = 0x7fff_ffff
+;     return v5
+; }
+
 function %icmp_sgt_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -613,6 +1031,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_sgt_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp sgt v0, v1
+    return v2
+}
+
+; function %icmp_sgt_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 1
+;     v2 = icmp sgt v0, v1  ; v1 = 1
+;     return v2
+; }
+
 function %icmp_sgt_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -627,6 +1059,20 @@ block0(v0: i32):
 ;     return v4
 ; }
 
+function %icmp_sgt_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp sgt v0, v1
+    return v2
+}
+
+; function %icmp_sgt_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp sgt v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_sgt_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -641,6 +1087,20 @@ block0(v0: i32):
 ;     return v3
 ; }
 
+function %icmp_sgt_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp sgt v0, v1
+    return v2
+}
+
+; function %icmp_sgt_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp sgt v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_sgt_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -654,6 +1114,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 0
 ; }
 
+function %icmp_sgt_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp sgt v0, v1
+    return v2
+}
+
+; function %icmp_sgt_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0x7fff_ffff
+;     v4 = icmp eq v0, v3  ; v3 = 0x7fff_ffff
+;     return v4
+; }
+
 function %icmp_sge_umin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0
@@ -668,6 +1142,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_sge_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp sge v0, v1
+    return v2
+}
+
+; function %icmp_sge_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v3 = iconst.i32 0
+;     v4 = icmp sgt v0, v3  ; v3 = 0
+;     return v4
+; }
+
 function %icmp_sge_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -682,6 +1170,20 @@ block0(v0: i32):
 ;     return v2
 ; }
 
+function %icmp_sge_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp sge v0, v1
+    return v2
+}
+
+; function %icmp_sge_umax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0xffff_fffe
+;     v2 = icmp sge v0, v1  ; v1 = 0xffff_fffe
+;     return v2
+; }
+
 function %icmp_sge_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -695,6 +1197,20 @@ block0(v0: i32):
 ;     return v3  ; v3 = 1
 ; }
 
+function %icmp_sge_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp sge v0, v1
+    return v2
+}
+
+; function %icmp_sge_smin_plus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x8000_0001
+;     v2 = icmp sge v0, v1  ; v1 = 0x8000_0001
+;     return v2
+; }
+
 function %icmp_sge_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -709,6 +1225,20 @@ block0(v0: i32):
 ;     return v3
 ; }
 
+function %icmp_sge_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp sge v0, v1
+    return v2
+}
+
+; function %icmp_sge_smax_minus_1(i32) -> i8 fast {
+; block0(v0: i32):
+;     v1 = iconst.i32 0x7fff_fffe
+;     v2 = icmp sge v0, v1  ; v1 = 0x7fff_fffe
+;     return v2
+; }
+
 function %icmp_and_eq_eq(i32, i32) -> i8 {
 block0(v0: i32, v1: i32):
     v2 = icmp eq v0, v1
diff --git a/cranelift/filetests/filetests/egraph/icmp.clif b/cranelift/filetests/filetests/egraph/icmp.clif
index 44f50201dbda..03f2350b2cf6 100644
--- a/cranelift/filetests/filetests/egraph/icmp.clif
+++ b/cranelift/filetests/filetests/egraph/icmp.clif
@@ -77,9 +77,9 @@ block0(v0: i16):
 
 ; function %slt_one(i16) -> i8 fast {
 ; block0(v0: i16):
-;     v3 = iconst.i16 0
-;     v4 = icmp sle v0, v3  ; v3 = 0
-;     return v4
+;     v1 = iconst.i16 1
+;     v9 = icmp slt v0, v1  ; v1 = 1
+;     return v9
 ; }
 
 function %uge_one(i32) -> i8 {
@@ -92,8 +92,8 @@ block0(v0: i32):
 ; function %uge_one(i32) -> i8 fast {
 ; block0(v0: i32):
 ;     v3 = iconst.i32 0
-;     v4 = icmp ne v0, v3  ; v3 = 0
-;     return v4
+;     v5 = icmp ne v0, v3  ; v3 = 0
+;     return v5
 ; }
 
 function %ult_one(i8) -> i8 {
diff --git a/cranelift/filetests/filetests/egraph/make-icmp-parameterized-tests.sh b/cranelift/filetests/filetests/egraph/make-icmp-parameterized-tests.sh
index ab6e5417539c..1b495080a27b 100755
--- a/cranelift/filetests/filetests/egraph/make-icmp-parameterized-tests.sh
+++ b/cranelift/filetests/filetests/egraph/make-icmp-parameterized-tests.sh
@@ -2,7 +2,7 @@
 
 set -e
 cd $(dirname "$0")
-out=parameterized-icmp.clif
+out=icmp-parameterized.clif
 CCS="eq ne ult ule ugt uge slt sle sgt sge"
 
 function main {
@@ -42,6 +42,13 @@ block0(v0: i32):
     return v2
 }
 
+function %icmp_${cc}_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = icmp ${cc} v0, v1
+    return v2
+}
+
 function %icmp_${cc}_umax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0xFFFF_FFFF
@@ -49,6 +56,13 @@ block0(v0: i32):
     return v2
 }
 
+function %icmp_${cc}_umax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0xFFFF_FFFE
+    v2 = icmp ${cc} v0, v1
+    return v2
+}
+
 function %icmp_${cc}_smin(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x8000_0000
@@ -56,6 +70,13 @@ block0(v0: i32):
     return v2
 }
 
+function %icmp_${cc}_smin_plus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x8000_0001
+    v2 = icmp ${cc} v0, v1
+    return v2
+}
+
 function %icmp_${cc}_smax(i32) -> i8 {
 block0(v0: i32):
     v1 = iconst.i32 0x7FFF_FFFF
@@ -63,6 +84,13 @@ block0(v0: i32):
     return v2
 }
 
+function %icmp_${cc}_smax_minus_1(i32) -> i8 {
+block0(v0: i32):
+    v1 = iconst.i32 0x7FFF_FFFE
+    v2 = icmp ${cc} v0, v1
+    return v2
+}
+
 EOF
     done
 
diff --git a/cranelift/filetests/filetests/egraph/spaceship.clif b/cranelift/filetests/filetests/egraph/spaceship.clif
index 7c1c8e2be099..de5eb9031717 100644
--- a/cranelift/filetests/filetests/egraph/spaceship.clif
+++ b/cranelift/filetests/filetests/egraph/spaceship.clif
@@ -425,8 +425,8 @@ block0(v0: i16, v1: i16):
     v5 = iconst.i8 0
     v6 = icmp sle v4, v5
     return v6
-    ; check: v7 = icmp sle v0, v1
-    ; check: return v7
+    ; check: v15 = icmp sle v0, v1
+    ; check: return v15
 }
 
 function %sgt_via_cmp(i32, i32) -> i8 {