diff --git a/lib/cretonne/meta/gen_instr.py b/lib/cretonne/meta/gen_instr.py
index e6eaa82c32..02677bfdbd 100644
--- a/lib/cretonne/meta/gen_instr.py
+++ b/lib/cretonne/meta/gen_instr.py
@@ -439,6 +439,7 @@ def gen_type_constraints(fmt, instrs):
                         get_constraint(i.ins[opnum], ctrl_typevar, type_sets))
             offset = operand_seqs.add(constraints)
             fixed_results = len(i.value_results)
+            fixed_values = len(i.value_opnums)
             # Can the controlling type variable be inferred from the designated
             # operand?
             use_typevar_operand = i.is_polymorphic and i.use_typevar_operand
@@ -449,10 +450,10 @@ def gen_type_constraints(fmt, instrs):
             # result?
             requires_typevar_operand = use_typevar_operand and not use_result
             fmt.comment(
-                    ('{}: fixed_results={}, use_typevar_operand={}, ' +
-                        'requires_typevar_operand={}')
+                    '{}: fixed_results={}, use_typevar_operand={}, '
+                    'requires_typevar_operand={}, fixed_values={}'
                     .format(i.camel_name, fixed_results, use_typevar_operand,
-                            requires_typevar_operand))
+                            requires_typevar_operand, fixed_values))
             fmt.comment('Constraints={}'.format(constraints))
             if i.is_polymorphic:
                 fmt.comment(
@@ -464,6 +465,8 @@ def gen_type_constraints(fmt, instrs):
                 flags |= 8
             if requires_typevar_operand:
                 flags |= 0x10
+            assert fixed_values < 8, "Bit field encoding too tight"
+            flags |= fixed_values << 5
 
             with fmt.indented('OpcodeConstraints {', '},'):
                 fmt.line('flags: {:#04x},'.format(flags))
diff --git a/lib/cretonne/src/ir/instructions.rs b/lib/cretonne/src/ir/instructions.rs
index de34a708c9..7e970f73b8 100644
--- a/lib/cretonne/src/ir/instructions.rs
+++ b/lib/cretonne/src/ir/instructions.rs
@@ -387,6 +387,9 @@ pub struct OpcodeConstraints {
     /// Bit 4:
     ///     This opcode is polymorphic and the controlling type variable does *not* appear as the
     ///     first result type.
+    ///
+    /// Bits 5-7:
+    ///     Number of fixed value arguments. The minimum required number of value operands.
     flags: u8,
 
     /// Permitted set of types for the controlling type variable as an index into `TYPE_SETS`.
@@ -423,6 +426,17 @@ impl OpcodeConstraints {
         (self.flags & 0x7) as usize
     }
 
+    /// Get the number of *fixed* input values required by this opcode.
+    ///
+    /// This does not include `variable_args` arguments on call and branch instructions.
+    ///
+    /// The number of fixed input values is usually implied by the instruction format, but
+    /// instruction formats that use a `ValueList` put both fixed and variable arguments in the
+    /// list. This method returns the *minimum* number of values required in the value list.
+    pub fn fixed_value_arguments(self) -> usize {
+        ((self.flags >> 5) & 0x7) as usize
+    }
+
     /// Get the offset into `TYPE_SETS` for the controlling type variable.
     /// Returns `None` if the instruction is not polymorphic.
     fn typeset_offset(self) -> Option<usize> {
@@ -609,6 +623,22 @@ mod tests {
         assert_eq!(mem::size_of::<InstructionData>(), 16);
     }
 
+    #[test]
+    fn constraints() {
+        let a = Opcode::Iadd.constraints();
+        assert!(a.use_typevar_operand());
+        assert_eq!(a.fixed_results(), 1);
+        assert_eq!(a.fixed_value_arguments(), 2);
+
+        let c = Opcode::Call.constraints();
+        assert_eq!(c.fixed_results(), 0);
+        assert_eq!(c.fixed_value_arguments(), 0);
+
+        let i = Opcode::CallIndirect.constraints();
+        assert_eq!(i.fixed_results(), 0);
+        assert_eq!(i.fixed_value_arguments(), 1);
+    }
+
     #[test]
     fn value_set() {
         use ir::types::*;