diff --git a/compiler/noirc_evaluator/src/ssa/opt/constant_folding.rs b/compiler/noirc_evaluator/src/ssa/opt/constant_folding.rs
index 4ec39de655d..c4c811cb900 100644
--- a/compiler/noirc_evaluator/src/ssa/opt/constant_folding.rs
+++ b/compiler/noirc_evaluator/src/ssa/opt/constant_folding.rs
@@ -242,10 +242,8 @@ impl<'brillig> Context<'brillig> {
             function.dfg.make_constant(FieldElement::one(), NumericType::bool());
 
         for instruction_id in instructions {
-            if !self.values_to_replace.is_empty() {
-                let instruction = &mut function.dfg[instruction_id];
-                instruction.replace_values(&self.values_to_replace);
-            }
+            let instruction = &mut function.dfg[instruction_id];
+            instruction.replace_values(&self.values_to_replace);
 
             self.fold_constants_into_instruction(
                 function,
@@ -256,11 +254,18 @@ impl<'brillig> Context<'brillig> {
             );
         }
 
+        // Map the block terminator, resolving any values in the terminator with the
+        // internal value mapping generated by this pass.
         function.dfg.replace_values_in_block_terminator(block_id, &self.values_to_replace);
         function.dfg.data_bus.replace_values(&self.values_to_replace);
 
         // Map a terminator in place, replacing any ValueId in the terminator with the
         // resolved version of that value id from the simplification cache's internal value mapping.
+        // We need this in addition to the value replacement above in order to take advantage
+        // of constraints that may have advised simplifications.
+        // The value mapping (`self.values_to_replace`) only maps old instruction results to new instruction results.
+        // However, constraints do not have "results" like other instructions, thus are not included in `self.values_to_replace`.
+        // To take advantage of constraint simplification we need to still resolve its cache.
         let mut terminator = function.dfg[block_id].take_terminator();
         terminator.map_values_mut(|value| {
             Self::resolve_cache(
@@ -271,6 +276,14 @@ impl<'brillig> Context<'brillig> {
             )
         });
         function.dfg[block_id].set_terminator(terminator);
+        function.dfg.data_bus.map_values_mut(|value| {
+            Self::resolve_cache(
+                block_id,
+                dom,
+                self.get_constraint_map(side_effects_enabled_var),
+                value,
+            )
+        });
 
         self.block_queue.extend(function.dfg[block_id].successors());
     }
@@ -845,7 +858,7 @@ fn has_side_effects(instruction: &Instruction, dfg: &DataFlowGraph) -> bool {
         // These can fail.
         Constrain(..) | ConstrainNotEqual(..) | RangeCheck { .. } => true,
 
-        // This should never be side-effectful
+        // This should never be side-effectual
         MakeArray { .. } | Noop => false,
 
         // Some binary math can overflow or underflow
@@ -1946,4 +1959,62 @@ mod test {
         }
         ");
     }
+
+    #[test]
+    fn constant_fold_terminator_argument_from_constrain() {
+        // The only instructions advising simplifications for v0 are
+        // constrain instructions. We want to make sure that those simplifications
+        // are still used for any terminator arguments.
+        let src = "
+        brillig(inline) predicate_pure fn main f0 {
+          b0(v0: Field, v1: Field):
+            v5 = eq v0, Field 1
+            constrain v0 == Field 1
+            v7 = eq v1, Field 0
+            constrain v1 == Field 0
+            v8 = truncate v0 to 32 bits, max_bit_size: 254
+            v9 = cast v8 as u32
+            v11 = eq v9, u32 0
+            jmpif v11 then: b1, else: b2
+          b1():
+            v13 = add v0, Field 1
+            jmp b3(v0, v13)
+          b2():
+            v12 = add v0, Field 1
+            jmp b3(v12, v0)
+          b3(v2: Field, v3: Field):
+            v14 = add v0, Field 1
+            v15 = eq v2, v14
+            constrain v2 == v14
+            v16 = eq v3, v0
+            constrain v3 == v0
+            return
+        }
+        ";
+
+        let ssa = Ssa::from_str(src).unwrap();
+        let ssa = ssa.fold_constants_using_constraints();
+
+        // The terminators of b1 and b2 should now have constant arguments
+        assert_ssa_snapshot!(ssa, @r"
+        brillig(inline) predicate_pure fn main f0 {
+          b0(v0: Field, v1: Field):
+            v5 = eq v0, Field 1
+            constrain v0 == Field 1
+            v7 = eq v1, Field 0
+            constrain v1 == Field 0
+            jmpif u1 0 then: b1, else: b2
+          b1():
+            jmp b3(Field 1, Field 2)
+          b2():
+            jmp b3(Field 2, Field 1)
+          b3(v2: Field, v3: Field):
+            v10 = eq v2, Field 2
+            constrain v2 == Field 2
+            v11 = eq v3, Field 1
+            constrain v3 == Field 1
+            return
+        }
+        ");
+    }
 }