diff --git a/ufl/algorithms/signature.py b/ufl/algorithms/signature.py
index ab9690bd6..4650818c1 100644
--- a/ufl/algorithms/signature.py
+++ b/ufl/algorithms/signature.py
@@ -43,7 +43,6 @@ def compute_terminal_hashdata(expressions, renumbering):
     # arguments, and just take repr of the rest of the terminals while
     # we're iterating over them
     terminal_hashdata = {}
-    labels = {}
     index_numbering = {}
     for expression in expressions:
         for expr in traverse_unique_terminals(expression):
@@ -69,12 +68,7 @@ def compute_terminal_hashdata(expressions, renumbering):
                 data = expr._ufl_signature_data_(renumbering)
 
             elif isinstance(expr, Label):
-                # Numbering labels as we visit them # TODO: Include in
-                # renumbering
-                data = labels.get(expr)
-                if data is None:
-                    data = "L%d" % len(labels)
-                    labels[expr] = data
+                data = expr._ufl_signature_data_(renumbering)
 
             elif isinstance(expr, ExprList):
                 # Not really a terminal but can have 0 operands...
diff --git a/ufl/coefficient.py b/ufl/coefficient.py
index d88743375..704c3912d 100644
--- a/ufl/coefficient.py
+++ b/ufl/coefficient.py
@@ -19,13 +19,13 @@
 from ufl.functionspace import AbstractFunctionSpace, FunctionSpace, MixedFunctionSpace
 from ufl.form import BaseForm
 from ufl.split_functions import split
-from ufl.utils.counted import counted_init
+from ufl.utils.counted import Counted
 from ufl.duals import is_primal, is_dual
 
 # --- The Coefficient class represents a coefficient in a form ---
 
 
-class BaseCoefficient(object):
+class BaseCoefficient(Counted):
     """UFL form argument type: Parent Representation of a form coefficient."""
 
     # Slots are disabled here because they cause trouble in PyDOLFIN
@@ -33,14 +33,13 @@ class BaseCoefficient(object):
     # __slots__ = ("_count", "_ufl_function_space", "_repr", "_ufl_shape")
     _ufl_noslots_ = True
     __slots__ = ()
-    _globalcount = 0
     _ufl_is_abstract_ = True
 
     def __getnewargs__(self):
         return (self._ufl_function_space, self._count)
 
     def __init__(self, function_space, count=None):
-        counted_init(self, count, Coefficient)
+        Counted.__init__(self, count, Coefficient)
 
         if isinstance(function_space, FiniteElementBase):
             # For legacy support for .ufl files using cells, we map
@@ -57,9 +56,6 @@ def __init__(self, function_space, count=None):
         self._repr = "BaseCoefficient(%s, %s)" % (
             repr(self._ufl_function_space), repr(self._count))
 
-    def count(self):
-        return self._count
-
     @property
     def ufl_shape(self):
         "Return the associated UFL shape."
@@ -111,6 +107,7 @@ class Cofunction(BaseCoefficient, BaseForm):
 
     __slots__ = (
         "_count",
+        "_counted_class",
         "_arguments",
         "_ufl_function_space",
         "ufl_operands",
@@ -118,7 +115,6 @@ class Cofunction(BaseCoefficient, BaseForm):
         "_ufl_shape",
         "_hash"
     )
-    # _globalcount = 0
     _primal = False
     _dual = True
 
@@ -161,7 +157,6 @@ class Coefficient(FormArgument, BaseCoefficient):
     """UFL form argument type: Representation of a form coefficient."""
 
     _ufl_noslots_ = True
-    _globalcount = 0
     _primal = True
     _dual = False
 
diff --git a/ufl/constant.py b/ufl/constant.py
index 66e7a8f33..2819647e3 100644
--- a/ufl/constant.py
+++ b/ufl/constant.py
@@ -11,17 +11,16 @@
 from ufl.core.ufl_type import ufl_type
 from ufl.core.terminal import Terminal
 from ufl.domain import as_domain
-from ufl.utils.counted import counted_init
+from ufl.utils.counted import Counted
 
 
 @ufl_type()
-class Constant(Terminal):
+class Constant(Terminal, Counted):
     _ufl_noslots_ = True
-    _globalcount = 0
 
     def __init__(self, domain, shape=(), count=None):
         Terminal.__init__(self)
-        counted_init(self, count=count, countedclass=Constant)
+        Counted.__init__(self, count, Constant)
 
         self._ufl_domain = as_domain(domain)
         self._ufl_shape = shape
@@ -31,9 +30,6 @@ def __init__(self, domain, shape=(), count=None):
         self._repr = "Constant({}, {}, {})".format(
             repr(self._ufl_domain), repr(self._ufl_shape), repr(self._count))
 
-    def count(self):
-        return self._count
-
     @property
     def ufl_shape(self):
         return self._ufl_shape
diff --git a/ufl/core/multiindex.py b/ufl/core/multiindex.py
index 9b9d15b8d..8d9c5dee6 100644
--- a/ufl/core/multiindex.py
+++ b/ufl/core/multiindex.py
@@ -10,7 +10,7 @@
 # Modified by Massimiliano Leoni, 2016.
 
 
-from ufl.utils.counted import counted_init
+from ufl.utils.counted import Counted
 from ufl.core.ufl_type import ufl_type
 from ufl.core.terminal import Terminal
 
@@ -70,20 +70,15 @@ def __repr__(self):
         return r
 
 
-class Index(IndexBase):
+class Index(IndexBase, Counted):
     """UFL value: An index with no value assigned.
 
     Used to represent free indices in Einstein indexing notation."""
-    __slots__ = ("_count",)
-
-    _globalcount = 0
+    __slots__ = ("_count", "_counted_class")
 
     def __init__(self, count=None):
         IndexBase.__init__(self)
-        counted_init(self, count, Index)
-
-    def count(self):
-        return self._count
+        Counted.__init__(self, count, Index)
 
     def __hash__(self):
         return hash(("Index", self._count))
diff --git a/ufl/form.py b/ufl/form.py
index 019c7c12f..eeff85020 100644
--- a/ufl/form.py
+++ b/ufl/form.py
@@ -16,12 +16,15 @@
 from itertools import chain
 
 from ufl.checks import is_scalar_constant_expression
+from ufl.constant import Constant
 from ufl.constantvalue import Zero
 from ufl.core.expr import Expr, ufl_err_str
 from ufl.core.ufl_type import UFLType, ufl_type
 from ufl.domain import extract_unique_domain, sort_domains
 from ufl.equation import Equation
 from ufl.integral import Integral
+from ufl.utils.counted import Counted
+from ufl.utils.sorting import sorted_by_count
 
 # Export list for ufl.classes
 __all_classes__ = ["Form", "BaseForm", "ZeroBaseForm"]
@@ -257,8 +260,9 @@ class Form(BaseForm):
         "_arguments",
         "_coefficients",
         "_coefficient_numbering",
-        "_constant_numbering",
         "_constants",
+        "_constant_numbering",
+        "_terminal_numbering",
         "_hash",
         "_signature",
         # --- Dict that external frameworks can place framework-specific
@@ -289,11 +293,10 @@ def __init__(self, integrals):
         self._coefficients = None
         self._coefficient_numbering = None
         self._constant_numbering = None
+        self._terminal_numbering = None
 
         from ufl.algorithms.analysis import extract_constants
         self._constants = extract_constants(self)
-        self._constant_numbering = dict(
-            (c, i) for i, c in enumerate(self._constants))
 
         # Internal variables for caching of hash and signature after
         # first request
@@ -406,8 +409,15 @@ def coefficients(self):
     def coefficient_numbering(self):
         """Return a contiguous numbering of coefficients in a mapping
         ``{coefficient:number}``."""
+        # cyclic import
+        from ufl.coefficient import Coefficient
+
         if self._coefficient_numbering is None:
-            self._analyze_form_arguments()
+            self._coefficient_numbering = {
+                expr: num
+                for expr, num in self.terminal_numbering().items()
+                if isinstance(expr, Coefficient)
+            }
         return self._coefficient_numbering
 
     def constants(self):
@@ -416,8 +426,38 @@ def constants(self):
     def constant_numbering(self):
         """Return a contiguous numbering of constants in a mapping
         ``{constant:number}``."""
+        if self._constant_numbering is None:
+            self._constant_numbering = {
+                expr: num
+                for expr, num in self.terminal_numbering().items()
+                if isinstance(expr, Constant)
+            }
         return self._constant_numbering
 
+    def terminal_numbering(self):
+        """Return a contiguous numbering for all counted objects in the form.
+
+        The returned object is mapping from terminal to its number (an integer).
+
+        The numbering is computed per type so :class:`Coefficient`s,
+        :class:`Constant`s, etc will each be numbered from zero.
+
+        """
+        # cyclic import
+        from ufl.algorithms.analysis import extract_type
+
+        if self._terminal_numbering is None:
+            exprs_by_type = defaultdict(set)
+            for counted_expr in extract_type(self, Counted):
+                exprs_by_type[counted_expr._counted_class].add(counted_expr)
+
+            numbering = {}
+            for exprs in exprs_by_type.values():
+                for i, expr in enumerate(sorted_by_count(exprs)):
+                    numbering[expr] = i
+            self._terminal_numbering = numbering
+        return self._terminal_numbering
+
     def signature(self):
         "Signature for use with jit cache (independent of incidental numbering of indices etc.)"
         if self._signature is None:
@@ -625,23 +665,19 @@ def _analyze_form_arguments(self):
             sorted(set(arguments), key=lambda x: x.number()))
         self._coefficients = tuple(
             sorted(set(coefficients), key=lambda x: x.count()))
-        self._coefficient_numbering = dict(
-            (c, i) for i, c in enumerate(self._coefficients))
 
     def _compute_renumbering(self):
         # Include integration domains and coefficients in renumbering
         dn = self.domain_numbering()
-        cn = self.coefficient_numbering()
-        cnstn = self.constant_numbering()
+        tn = self.terminal_numbering()
         renumbering = {}
         renumbering.update(dn)
-        renumbering.update(cn)
-        renumbering.update(cnstn)
+        renumbering.update(tn)
 
         # Add domains of coefficients, these may include domains not
         # among integration domains
         k = len(dn)
-        for c in cn:
+        for c in self.coefficients():
             d = extract_unique_domain(c)
             if d is not None and d not in renumbering:
                 renumbering[d] = k
diff --git a/ufl/matrix.py b/ufl/matrix.py
index bd3a25d91..0b120f414 100644
--- a/ufl/matrix.py
+++ b/ufl/matrix.py
@@ -13,24 +13,24 @@
 from ufl.core.ufl_type import ufl_type
 from ufl.argument import Argument
 from ufl.functionspace import AbstractFunctionSpace
-from ufl.utils.counted import counted_init
+from ufl.utils.counted import Counted
 
 
 # --- The Matrix class represents a matrix, an assembled two form ---
 
 @ufl_type()
-class Matrix(BaseForm):
+class Matrix(BaseForm, Counted):
     """An assemble linear operator between two function spaces."""
 
     __slots__ = (
         "_count",
+        "_counted_class",
         "_ufl_function_spaces",
         "ufl_operands",
         "_repr",
         "_hash",
         "_ufl_shape",
         "_arguments")
-    _globalcount = 0
 
     def __getnewargs__(self):
         return (self._ufl_function_spaces[0], self._ufl_function_spaces[1],
@@ -38,7 +38,7 @@ def __getnewargs__(self):
 
     def __init__(self, row_space, column_space, count=None):
         BaseForm.__init__(self)
-        counted_init(self, count, Matrix)
+        Counted.__init__(self, count, Matrix)
 
         if not isinstance(row_space, AbstractFunctionSpace):
             raise ValueError("Expecting a FunctionSpace as the row space.")
@@ -52,9 +52,6 @@ def __init__(self, row_space, column_space, count=None):
         self._hash = None
         self._repr = f"Matrix({self._ufl_function_spaces[0]!r}, {self._ufl_function_spaces[1]!r}, {self._count!r})"
 
-    def count(self):
-        return self._count
-
     def ufl_function_spaces(self):
         "Get the tuple of function spaces of this coefficient."
         return self._ufl_function_spaces
diff --git a/ufl/utils/counted.py b/ufl/utils/counted.py
index 66d3fd79f..f04bc2aca 100644
--- a/ufl/utils/counted.py
+++ b/ufl/utils/counted.py
@@ -1,5 +1,5 @@
 # -*- coding: utf-8 -*-
-"Utilites for types with a global unique counter attached to each object."
+"Mixin class for types with a global unique counter attached to each object."
 
 # Copyright (C) 2008-2016 Martin Sandve Alnæs
 #
@@ -7,37 +7,34 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
+import itertools
 
-def counted_init(self, count=None, countedclass=None):
-    "Initialize a counted object, see ExampleCounted below for how to use."
 
-    if countedclass is None:
-        countedclass = type(self)
+class Counted:
+    """Mixin class for globally counted objects."""
 
-    if count is None:
-        count = countedclass._globalcount
+    # Mixin classes do not work well with __slots__ so _count must be
+    # added to the __slots__ of the inheriting class
+    __slots__ = ()
 
-    self._count = count
+    _counter = None
 
-    if self._count >= countedclass._globalcount:
-        countedclass._globalcount = self._count + 1
+    def __init__(self, count=None, counted_class=None):
+        """Initialize the Counted instance.
 
+        :arg count: The object count, if ``None`` defaults to the next value
+                    according to the global counter (per type).
+        :arg counted_class: Class to attach the global counter too. If ``None``
+                            then ``type(self)`` will be used.
 
-class ExampleCounted(object):
-    """An example class for classes of objects identified by a global counter.
+        """
+        # create a new counter for each subclass
+        counted_class = counted_class or type(self)
+        if counted_class._counter is None:
+            counted_class._counter = itertools.count()
 
-    Mimic this class to create globally counted objects within a single type.
-    """
-    # Store the count for each object
-    __slots__ = ("_count",)
+        self._count = count if count is not None else next(counted_class._counter)
+        self._counted_class = counted_class
 
-    # Store a global counter with the class
-    _globalcount = 0
-
-    # Call counted_init with an optional constructor argument and the class
-    def __init__(self, count=None):
-        counted_init(self, count, ExampleCounted)
-
-    # Make the count accessible
     def count(self):
         return self._count
diff --git a/ufl/variable.py b/ufl/variable.py
index 1b68d6c06..b5a29dc26 100644
--- a/ufl/variable.py
+++ b/ufl/variable.py
@@ -8,7 +8,7 @@
 #
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
-from ufl.utils.counted import counted_init
+from ufl.utils.counted import Counted
 from ufl.core.expr import Expr
 from ufl.core.ufl_type import ufl_type
 from ufl.core.terminal import Terminal
@@ -17,17 +17,12 @@
 
 
 @ufl_type()
-class Label(Terminal):
-    __slots__ = ("_count",)
-
-    _globalcount = 0
+class Label(Terminal, Counted):
+    __slots__ = ("_count", "_counted_class")
 
     def __init__(self, count=None):
         Terminal.__init__(self)
-        counted_init(self, count, Label)
-
-    def count(self):
-        return self._count
+        Counted.__init__(self, count, Label)
 
     def __str__(self):
         return "Label(%d)" % self._count
@@ -55,6 +50,9 @@ def ufl_domains(self):
         "Return tuple of domains related to this terminal object."
         return ()
 
+    def _ufl_signature_data_(self, renumbering):
+        return ("Label", renumbering[self])
+
 
 @ufl_type(is_shaping=True, is_index_free=True, num_ops=1, inherit_shape_from_operand=0)
 class Variable(Operator):