In this paper we describe and verify a method, called SMIP, to circumvent the trade-off between motion blur and noise, specifically for scenes with predominantly two distinct linear motions (sparse motion). This is based on employing image stabilization hardware to track objects during exposure while capturing two images in quick succession. The two images are combined into a single sharp image without segmentation or local motion estimation. We provide a theoretical analysis and simulations to show that the Signal-to-Noise Ratio (SNR) increases up to 20 dB over conventional short-exposure photography. We demonstrate that the proposed method significantly improves the SNR compared to existing methods. Furthermore, we evaluate a proof-of-concept using modified off-the-shelf optical image stabilization hardware to verify the effectiveness of our method in practice, showing a good correspondence between the simulation and practical results.