Parameter estimation for the K distribution is an essential part of the statistical analysis of non-Rayleigh sonar reverberation and clutter for performance prediction, estimation of scattering properties, and for use in signal and information processing algorithms. Owing to the computational intensity of maximum likelihood techniques, the method of moments is often used to obtain parameter estimates. However, as often as half the time these techniques will result in non-invertible moment equations and therefore no estimate of the K-distribution parameters. In this paper a method-of-moments estimator is proposed that always provides a solution by exploiting bootstrapping to obtain a probability density function for the K-distribution shape parameter (alpha) given the observed data from which the mean or a confidence interval may be computed. The bootstrap-based estimate is seen to have lower mean squared error than the method of moments with minimal additional computational effort. The technique is also shown to easily extend to the combination of multiple independent observations providing better estimation than taking a mean or median when alpha is moderate to large