diff --git a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
index 7b40c35960a..5d19f9629ba 100644
--- a/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
+++ b/acvm-repo/acvm/src/compiler/optimizers/redundant_range.rs
@@ -48,25 +48,51 @@ impl RangeOptimizer {
     /// only store the fact that we have constrained it to
     /// be 16 bits.
     fn collect_ranges(circuit: &Circuit) -> BTreeMap<Witness, u32> {
-        let mut witness_to_bit_sizes = BTreeMap::new();
+        let mut witness_to_bit_sizes: BTreeMap<Witness, u32> = BTreeMap::new();
 
         for opcode in &circuit.opcodes {
-            // Extract the witness index and number of bits,
-            // if it is a range constraint
-            let (witness, num_bits) = match extract_range_opcode(opcode) {
-                Some(func_inputs) => func_inputs,
-                None => continue,
+            let Some((witness, num_bits)) = (match opcode {
+                Opcode::AssertZero(expr) => {
+                    // If the opcode is constraining a witness to be equal to a value then it can be considered
+                    // as a range opcode for the number of bits required to hold that value.
+                    if expr.is_degree_one_univariate() {
+                        let (k, witness) = expr.linear_combinations[0];
+                        let constant = expr.q_c;
+                        let witness_value = -constant / k;
+
+                        if witness_value.is_zero() {
+                            Some((witness, 0))
+                        } else {
+                            // We subtract off 1 bit from the implied witness value to give the weakest range constraint
+                            // which would be stricter than the constraint imposed by this opcode.
+                            let implied_range_constraint_bits = witness_value.num_bits() - 1;
+                            Some((witness, implied_range_constraint_bits))
+                        }
+                    } else {
+                        None
+                    }
+                }
+
+
+                Opcode::BlackBoxFuncCall(BlackBoxFuncCall::RANGE {
+                    input: FunctionInput { witness, num_bits },
+                }) => {
+                    Some((*witness, *num_bits))
+                }
+
+                _ => None,
+            }) else {
+                continue;
             };
 
             // Check if the witness has already been recorded and if the witness
             // size is more than the current one, we replace it
-            let should_replace = match witness_to_bit_sizes.get(&witness).copied() {
-                Some(old_range_bits) => old_range_bits > num_bits,
-                None => true,
-            };
-            if should_replace {
-                witness_to_bit_sizes.insert(witness, num_bits);
-            }
+            witness_to_bit_sizes
+                .entry(witness)
+                .and_modify(|old_range_bits| {
+                    *old_range_bits = std::cmp::min(*old_range_bits, num_bits);
+                })
+                .or_insert(num_bits);
         }
         witness_to_bit_sizes
     }
@@ -116,16 +142,10 @@ impl RangeOptimizer {
 /// Extract the range opcode from the `Opcode` enum
 /// Returns None, if `Opcode` is not the range opcode.
 fn extract_range_opcode(opcode: &Opcode) -> Option<(Witness, u32)> {
-    // Range constraints are blackbox function calls
-    // so we first extract the function call
-    let func_call = match opcode {
-        acir::circuit::Opcode::BlackBoxFuncCall(func_call) => func_call,
-        _ => return None,
-    };
-
-    // Skip if it is not a range constraint
-    match func_call {
-        BlackBoxFuncCall::RANGE { input } => Some((input.witness, input.num_bits)),
+    match opcode {
+        Opcode::BlackBoxFuncCall(BlackBoxFuncCall::RANGE { input }) => {
+            Some((input.witness, input.num_bits))
+        }
         _ => None,
     }
 }
@@ -246,4 +266,17 @@ mod tests {
         let (optimized_circuit, _) = optimizer.replace_redundant_ranges(acir_opcode_positions);
         assert_eq!(optimized_circuit.opcodes.len(), 5);
     }
+
+    #[test]
+    fn constant_implied_ranges() {
+        // The optimizer should use knowledge about constant witness assignments to remove range opcodes.
+        let mut circuit = test_circuit(vec![(Witness(1), 16)]);
+
+        circuit.opcodes.push(Opcode::AssertZero(Witness(1).into()));
+        let acir_opcode_positions = circuit.opcodes.iter().enumerate().map(|(i, _)| i).collect();
+        let optimizer = RangeOptimizer::new(circuit);
+        let (optimized_circuit, _) = optimizer.replace_redundant_ranges(acir_opcode_positions);
+        assert_eq!(optimized_circuit.opcodes.len(), 1);
+        assert_eq!(optimized_circuit.opcodes[0], Opcode::AssertZero(Witness(1).into()));
+    }
 }