We present further extensions of yet another steganographic scheme (YASS), a method based on embedding data in randomized locations so as to resist blind steganalysis. YASS is a JPEG steganographic technique that hides data in the discrete cosing transform (DCT) coefficients of randomly chosen image blocks. Continuing to focus on JPEG image steganography, we present, in this paper, a further study on YASS with the goal of improving the rate of embedding. Following are the two main improvements presented in this paper: (i) a method that randomizes the quantization matrix used on the transform domain coefficients, and (ii) an iterative hiding method that utilizes the fact that the JPEG "attack" that causes errors in the hidden bits is actually known to the encoder. We show that using both these approaches, the embedding rate can be increased while maintaining the same level of undetectability (as the original YASS scheme). Moreover, for the same embedding rate, the proposed steganographic schemes are more undetectable than the popular matrix embedding based F5 scheme, using features proposed by Pevny and Fridrich for blind steganalysis.