A new constrained interpolation profile method, which is stable and accurate but requires less amount of computation, is provided. CIP is a high-order fluid advection solver that can reproduce rich details of fluids. It has third-order accuracy but its computation is performed over a compact stencil. A novel modification of the original CIP method that fixes all of the above problems without increasing the computational load or reducing the accuracy is provided. The proposed method brings significant improvements in both accuracy and speed.