diff --git a/compiler/noirc_evaluator/src/ssa.rs b/compiler/noirc_evaluator/src/ssa.rs
index 0e3076923e..e2da5652fa 100644
--- a/compiler/noirc_evaluator/src/ssa.rs
+++ b/compiler/noirc_evaluator/src/ssa.rs
@@ -63,6 +63,7 @@ pub(crate) fn optimize_into_acir(
         .run_pass(Ssa::mem2reg, "After Mem2Reg:")
         .run_pass(Ssa::fold_constants, "After Constant Folding:")
         .run_pass(Ssa::dead_instruction_elimination, "After Dead Instruction Elimination:")
+        .run_pass(Ssa::bubble_up_constrains, "After Constraint Bubbling:")
         .finish();
 
     let brillig = ssa.to_brillig(print_brillig_trace);
diff --git a/compiler/noirc_evaluator/src/ssa/opt/bubble_up_constrains.rs b/compiler/noirc_evaluator/src/ssa/opt/bubble_up_constrains.rs
new file mode 100644
index 0000000000..e0144005a0
--- /dev/null
+++ b/compiler/noirc_evaluator/src/ssa/opt/bubble_up_constrains.rs
@@ -0,0 +1,43 @@
+use crate::ssa::{ir::instruction::Instruction, ssa_gen::Ssa};
+
+impl Ssa {
+    /// A simple SSA pass to go through each instruction and move every `Instruction::Constrain` to immediately
+    /// after when all of its inputs are available.
+    #[tracing::instrument(level = "trace", skip(self))]
+    pub(crate) fn bubble_up_constrains(mut self) -> Ssa {
+        for function in self.functions.values_mut() {
+            for block in function.reachable_blocks() {
+                let instructions = function.dfg[block].take_instructions();
+                let mut filtered_instructions = Vec::with_capacity(instructions.len());
+
+                let dfg = &function.dfg;
+                for instruction in instructions {
+                    let (lhs, rhs) = match dfg[instruction] {
+                        Instruction::Constrain(lhs, rhs, ..) => (lhs, rhs),
+                        _ => {
+                            filtered_instructions.push(instruction);
+                            continue;
+                        }
+                    };
+
+                    let index = filtered_instructions
+                        .iter()
+                        .rev()
+                        .position(|instruction_id| {
+                            let results = dfg.instruction_results(*instruction_id).to_vec();
+                            results.contains(&lhs) || results.contains(&rhs)
+                        })
+                        // We iterate through the previous instructions in reverse order so the index is from the
+                        // back of the vector. Subtract from vector length to get correct index.
+                        .map(|reversed_index| filtered_instructions.len() - reversed_index)
+                        .unwrap_or(filtered_instructions.len());
+
+                    filtered_instructions.insert(index, instruction);
+                }
+
+                *function.dfg[block].instructions_mut() = filtered_instructions;
+            }
+        }
+        self
+    }
+}
diff --git a/compiler/noirc_evaluator/src/ssa/opt/mod.rs b/compiler/noirc_evaluator/src/ssa/opt/mod.rs
index 4d003c0594..71725422a7 100644
--- a/compiler/noirc_evaluator/src/ssa/opt/mod.rs
+++ b/compiler/noirc_evaluator/src/ssa/opt/mod.rs
@@ -5,6 +5,7 @@
 //! Generally, these passes are also expected to minimize the final amount of instructions.
 mod array_use;
 mod assert_constant;
+mod bubble_up_constrains;
 mod constant_folding;
 mod defunctionalize;
 mod die;