Humans and animals readily utilize active sensing, or the use of self-motion, to focus sensory and cognitive resources on the behaviorally most relevant stimuli and events in the environment. Understanding the computational basis of natural active sensing is important both for advancing brain sciences and for developing more powerful artificial systems. Recently, a goal-directed, context-sensitive, Bayesian control strategy for active sensing, termed C-DAC (Context-Dependent Active Controller), was proposed (Ahmad & Yu, 2013). In contrast to previously proposed algorithms for human active vision, which tend to optimize abstract statistical objectives and therefore cannot adapt to changing behavioral context or task goals, C-DAC directly minimizes behavioral costs and thus, automatically adapts itself to different task conditions. However, C-DAC is limited as a model of human active sensing, given its computational/representational requirements, especially for more complex, real-world situations. Here, we propose a myopic approximation to C-DAC, which also takes behavioral costs into account, but achieves a significant reduction in complexity by looking only one step ahead. We also present data from a human active visual search experiment, and compare the performance of the various models against human behavior. We find that C-DAC and its myopic variant both achieve better fit to human data than Infomax (Butko & Movellan, 2010), which maximizes expected cumulative future information gain. In summary, this work provides novel experimental results that differentiate theoretical models for human active sensing, as well as a novel active sensing algorithm that retains the context-sensitivity of the optimal controller while achieving significant computational savings.