diff --git a/CHANGELOG.md b/CHANGELOG.md
index bce0b6613..2a318611a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,7 @@
 
 ### Improvements
 - #325 Reduce memory consumption during inlining
+- #339 Reduce memory consumption under `Constraints` optimization goal
 
 ### Bug fixes
 
diff --git a/relations/src/r1cs/constraint_system.rs b/relations/src/r1cs/constraint_system.rs
index 93b37bfd3..03c5d1073 100644
--- a/relations/src/r1cs/constraint_system.rs
+++ b/relations/src/r1cs/constraint_system.rs
@@ -249,6 +249,58 @@ impl<F: Field> ConstraintSystem<F> {
         Ok(var)
     }
 
+    /// Optimized routine for multiplying a variable by a constant `other`.
+    #[inline]
+    pub fn mul_var_by_constant(
+        &mut self,
+        var: &Variable,
+        other: &F,
+    ) -> crate::r1cs::Result<Variable> {
+        // Create a new symbolic LC using this constant, deferring the inlining
+        // until the finalization phase.
+        #[inline]
+        fn base_mul_by_constant<F: Field>(
+            cs: &mut ConstraintSystem<F>,
+            var: &Variable,
+            other: F,
+        ) -> crate::r1cs::Result<Variable> {
+            let variable = cs.new_lc(lc!() + (other, *var)).unwrap();
+            Ok(variable)
+        }
+
+        return match var {
+            Variable::Zero => Ok(Variable::Zero),
+            Variable::One => base_mul_by_constant(self, var, *other),
+            Variable::Instance(_) => base_mul_by_constant(self, var, *other),
+            Variable::Witness(_) => base_mul_by_constant(self, var, *other),
+            Variable::SymbolicLc(index) => {
+                if self.optimization_goal == OptimizationGoal::Constraints
+                    || self.optimization_goal == OptimizationGoal::None
+                {
+                    // In this case we are optimizing for the number of constraints,
+                    // so we have no need for symbolic variables of intermediate computation steps.
+                    // Thus we inline this multiplication by a constant immediately.
+                    let lc = self.lc_map.get(&index).unwrap();
+                    let mut new_lc = lc.clone();
+                    for i in 0..new_lc.len() {
+                        new_lc[i].0 *= other;
+                    }
+                    let variable = self.new_lc(new_lc).unwrap();
+                    return Ok(variable);
+                } else {
+                    // In this case we are optimizing for constraint density,
+                    // so we want to know when a symbolic LC is being re-used.
+                    base_mul_by_constant(self, var, *other)
+                    // TODO: If `var` is a symbolic LC with a single element,
+                    // we don't need to make the new symbolic LC nest on top of var.
+                    // It can instead re-use the single variable underlying `var`.
+                    // This costs us an extra lookup though, so we should only do such
+                    // a switch if benchmarks prove it to be useful.
+                }
+            }
+        };
+    }
+
     /// Enforce a R1CS constraint with the name `name`.
     #[inline]
     pub fn enforce_constraint(