Improvements to two widely used particle-image velocimetry (PIV) algorithms, e.g., multi-grid and iterative image deformation cross-correlations, are proposed here to reduce the computational costs associated with time-resolved PIV (TR-PIV) data-processing. TR-PIV typically involves capturing significant time-series particle-image datasets across to allow statistically meaningful temporal and spectral analyses; hence considerable computational cost-savings can be realised. The improvements involve using the historical particle displacement field and its variation to determine the required window offsets and image deformations in the above-mentioned algorithms, respectively. In this case, cross-correlation based on the smallest interrogation window size can be used directly instead of multi-pass cross-correlations based on decreasing interrogation window sizes. To evaluate their efficacy, the proposed improvements were implemented and evaluated using synthetic PIV images of a Rankine vortex flow, numerical solutions for a square cylinder wake flow, as well as actual experimental time-series TR-PIV measurements. Comparisons show that the proposed improvements save up to 50% computational time while maintaining relatively similar measurement accuracy levels as conventional algorithms. In particular, the new algorithms successfully resolve unsteady flow fields where particle displacements vary by more than 20% between successive particle-images, where error propagations associated with large displacement variations are mitigated by employing suitable recalculation thresholds.