diff --git a/meta/cretonne/__init__.py b/meta/cretonne/__init__.py
index a5e842dd8e..d265009005 100644
--- a/meta/cretonne/__init__.py
+++ b/meta/cretonne/__init__.py
@@ -8,6 +8,7 @@ from __future__ import absolute_import
 import re
 import importlib
 from collections import namedtuple
+from .predicates import And
 
 
 camel_re = re.compile('(^|_)([a-z])')
@@ -1010,9 +1011,11 @@ class Encoding(object):
                  being encoded.
     :param recipe: The :py:class:`EncRecipe` to use.
     :param encbits: Additional encoding bits to be interpreted by `recipe`.
+    :param instp: Instruction predicate, or `None`.
+    :param isap: ISA predicate, or `None`.
     """
 
-    def __init__(self, cpumode, inst, recipe, encbits):
+    def __init__(self, cpumode, inst, recipe, encbits, instp=None, isap=None):
         assert isinstance(cpumode, CPUMode)
         assert isinstance(recipe, EncRecipe)
         self.inst, self.typevars = inst.fully_bound()
@@ -1022,6 +1025,9 @@ class Encoding(object):
                     self.inst.format, recipe.format))
         self.recipe = recipe
         self.encbits = encbits
+        # Combine recipe predicates with the manually specified ones.
+        self.instp = And.combine(recipe.instp, instp)
+        self.isap = And.combine(recipe.isap, instp)
 
     @staticmethod
     def _to_type_tuple(x):
diff --git a/meta/cretonne/predicates.py b/meta/cretonne/predicates.py
index 71a17eb01b..d6cb8f8b96 100644
--- a/meta/cretonne/predicates.py
+++ b/meta/cretonne/predicates.py
@@ -95,6 +95,22 @@ class And(Predicate):
             s = '({})'.format(s)
         return s
 
+    @staticmethod
+    def combine(*args):
+        """
+        Combine a sequence of predicates, allowing for `None` members.
+
+        Return a predicate that is true when all non-`None` arguments are true,
+        or `None` if all of the arguments are `None`.
+        """
+        args = tuple(p for p in args if p)
+        if args == ():
+            return None
+        if len(args) == 1:
+            return args[0]
+        # We have multiple predicate args. Combine with `And`.
+        return And(*args)
+
 
 class Or(Predicate):
     """