Recent positive selection can result in an excess of long identity-by-descent (IBD) haplotype segments. The statistical methods that we propose here address three major objectives in studying classical selective sweeps: scanning for regions of interest, identifying possible sweeping alleles, and estimating a selection coefficients. First, we implement a selection scan to locate regions of excess IBD rate. Second, we develop a statistic to rank alleles in strong linkage disequilibrium with a putative sweeping allele. We aggregate these scores to estimate the allele frequency of the sweeping allele, even if it is not genotyped. Lastly, we propose an estimator for the selection coefficient and quantify uncertainty using the parametric bootstrap. Comparing against state-of-the-art methods in extensive simulations, we show that our methods are better at pinpointing alleles at low frequency and estimatings≥ 0.015. We apply these methods to study positive selection in inferred European ancestry samples from the TOPMed project. We find twelve loci where their IBD rates exceed four standard deviations above the population median. The excess IBD rate at LCT is thirty-five standard deviations above the population median, and our estimates of its selection coefficient imply strong selection within the past 120 to 163 generations. Overall, we present robust and accurate new approaches to study very recent adaptive evolution under mild assumptions.