In this paper, we propose new adaptive search range motion estimation methods where the search ranges are constrained by the probabilities of motion vector differences and a search point sampling technique is applied to the constrained search ranges. Our new methods are based on our previous work, in which the search ranges were analytically determined by the probabilities. Since the proposed adaptive search range motion estimation methods effectively restrict the search ranges instead of search point sampling patterns, they provide a very flexible and hardware-friendly approach in motion estimation. The proposed methods were evaluated and tested with JM16.2 of the H.264/AVC video coding standard. Experiment results exhibit that with negligible degradation in PSNR, the proposed methods considerably reduce the computational complexity in comparison with the conventional methods. In particular, the combined method provides performance similar to that of the hybrid unsymmetrical-cross multi-hexagon-grid search method and outstanding merits in hardware implementation.