This paper studies computational improvement of the Gaussian Markov improvement algorithm (GMIA) whose underlying response surface model is a Gaussian Markov random field (GMRF). GMIA's computational bottleneck lies in the sampling decision, which requires factorizing and inverting a sparse, but large precision matrix of the GMRF at every iteration. We propose smart GMIA (sGMIA) that performs expensive linear algebraic operations intermittently, while recursively updating the vectors and matrices necessary to make sampling decisions for several iterations in between. The latter iterations are much cheaper than the former at the beginning, but their costs increase as the recursion continues and ultimately surpass the cost of the former. sGMIA adaptively decides how long to continue the recursion by minimizing the average per-iteration cost. We perform a floating-point operation analysis to demonstrate the computational benefit of sGMIA. Experiment results show that sGMIA enjoys computational efficiency while achieving the same search effectiveness as GMIA.