Separately optimizing different video coding technologies simplifies the implementation of coding algorithms, but it results in slowdown by not taking their internal relation into consideration. An integrated algorithm is proposed to jointly improve the speed of fractional pixel interpolation (FPI) and fractional pixel motion estimation (FPME) for HEVC. Different fractional pixels are distinguished by their interpolation filters to construct a FPME algorithm with the knowledge of their interpolation cost. The FPME algorithm produces a cost effective order for refinement search which checks fractional search positions (SPs) by not only maximizing the expectation for the R-D gains but also minimizing the computational cost at the same time. On the other hand, an on-demand FPI algorithm for HEVC is also proposed to save redundant interpolation as well as reduce duplicate calculation. Experimental results show that the introduced algorithm significantly improves the overall speed of FPME and FPI with negligible coding lost.