Smoothing filters have been used for pre/post-processing in various fields, such as computer vision and computer graphics. Bilateral filtering (BF) has a typical edge-preserving filter for such applications. The main issue of BF is its computational cost. Constant-time BF (O(1) BF) is one of the solutions to this problem, and compressive BF is a kind of O(1) BF. Compressive BF has, however, a restriction that we can only use Gaussian kernel as a range kernel until now. In this paper, we propose the method to extend compressive BF to handle arbitrary range kernels. Experimental results show that our extension handles arbitrary range kernels, and becomes the number of convolutions into half.