SummaryImage watermarking in wavelet domain is a challenging problem as it includes a proper selection of wavelet transforms as well as sub‐bands for accurate embedding and recovery of watermarks. However, selection of a suitable wavelet transform for multiple image watermarking is an area of great interest. Therefore, in this work, a multiple watermarking technique using combination of redundant discrete wavelet transforms (RDWT), non‐subsampled contourlet transform (NSCT), set partitioning in hierarchical tree (SPIHT), and singular value decomposition (SVD) is proposed. The proposed scheme is aimed to achieve high capacity, robustness, and imperceptibility. The security aspect of the proposed method is enhanced by using Arnold transform. Since RDWT and NSCT are both shift invariant in nature, therefore they are suitable for multiple image watermarking. Furthermore, the proposed method provides flexibility in selection of appropriate sub‐bands for watermark embedding and recovery. Experimental results and analysis reveals that the proposed technique gives maximum PSNR, NC, and SSIM value up to 40.97 dB, 1, and 0.9994, respectively. Furthermore, the performance estimation of our technique is found superior to previously reported techniques under consideration.