Ambiguity function shaping continues to be one of the most challenging open problems in cognitive radar. Analytically, a complex quartic function should be optimized as a function of the radar waveform code. Practical considerations further require that the waveform be constant modulus, which exacerbates the issue and leads to a hard non-convex problem. We develop a new approach called Adaptive Sequential Refinement (ASR) to suppress the clutter returns for a desired range-Doppler, i.e. ambiguity function response. ASR solves the aforementioned optimization problem in a unique iterative manner such that the formulation is updated depending on the iteration index. We establish formally that: 1.) the problem in each step of the iteration has a closed form solution, and 2.) monotonic decrease of the cost function until convergence is guaranteed. Experimental validation shows that ASR produces a radar waveform with higher Signal to Interference Ratio (SIR) and superior ambiguity function shaping than state of the art alternatives even as its computational burden is orders of magnitude lower.