This study investigates and enhances the corrective capability of small-sized tool influence functions （TIFs） in addressing form errors with spatial wavelengths comparable to their dimensions， through the analysis and optimization of millimeter spot-sized ion beam figuring （IBF）. A radial shell ribs evaluation method was established to quantify the corrective performance of small-sized TIFs across multiple frequencies， employing root-mean-square density （RMSD） distribution， convergence rates， and periodic surface processing outcomes. Based on this framework， a dwell time compensation strategy incorporating high-pass filtering was developed， resulting in improved convergence rates within the target spatial frequency bands. Experimental results demonstrate that the radial shell ribs analysis provides an efficient and convenient approach to evaluating TIF corrective capability across frequencies. The introduced dwell time compensation method significantly enhances the single-cycle convergence rate of small-sized TIFs within their effective frequency range. Specifically， for the critical frequency band associated with corrective capacity transitions （0.186 to 0.385 mm⁻¹）， the average convergence rate of a 2-mm full width at half maximum （FWHM） TIF increased from 76.4% to 91.7%. This approach enables consistent convergence of form errors throughout the entire frequency spectrum during processing with a single TIF， thereby advancing the manufacturing of high-precision optical components.