Selective sweeps are typically associated with a local reduction of genetic 
diversity around the adaptive site. However, selective sweeps can also quickly 
carry neutral mutations to observable population frequencies if they arise early 
in a sweep and hitchhike with the adaptive allele. We show that the interplay 
between mutation and exponential amplification through hitchhiking results in a 
characteristic frequency spectrum of the resulting novel haplotype variation 
that depends only on the ratio of the mutation rate and the selection 
coefficient of the sweep. On the basis of this result, we develop an estimator 
for the selection coefficient driving a sweep. Since this estimator utilizes the 
novel variation arising from mutations during a sweep, it does not rely on 
preexisting variation and can also be applied to loci that lack recombination. 
Compared with standard approaches that infer selection coefficients from the 
size of dips in genetic diversity around the adaptive site, our estimator 
requires much shorter sequences but sampled at high population depth to capture 
low-frequency variants; given such data, it consistently outperforms standard 
approaches. We investigate analytically and numerically how the accuracy of our 
estimator is affected by the decay of the sweep pattern over time as a 
consequence of random genetic drift and discuss potential effects of 
recombination, soft sweeps, and demography. As an example for its use, we apply 
our estimator to deep sequencing data from human immunodeficiency virus 
populations.