Perceptual image hashing has become increasingly popular for copy detection and indexing in digital photography. While many researchers have focused on proposing image hashing algorithms that are robust under a variety of content-preserving attacks, little attention has been paid to some of the relevant practical issues, such as estimating the parameter values for these algorithms and improving their speed. The present work addresses these concerns by automatic parameter estimation for the recently proposed fast Johnson- Lindenstrauss transform (FJLT) image hashing algorithm. Our simulation results using benchmark images manipulated under content-preserving operations demonstrate that the proposed algorithm finds a set of parameter values that make FJLT-based image hashing significantly faster, while achieving high performance.