This paper explores learned image compression based on traditional and learned discrete wavelet transform (DWT) architectures and learned entropy models for coding DWT subband coefficients. A learned DWT is obtained through the lifting scheme with learned nonlinear predict and update filters. Several learned entropy models, with varying computational complexities, are explored to exploit inter- and intra-DWT subband coefficient dependencies, akin to traditional EZW, SPIHT, or EBCOT algorithms. Experimental results show that when the explored learned entropy models are combined with traditional wavelet filters, such as the CDF 9/7 filters, compression performance that far exceeds that of JPEG2000 can be achieved. When the learned entropy models are combined with the learned DWT, compression performance increases further. The computations in the learned DWT and all entropy models, except one, can be simply parallelized, and thus, the systems provide practical encoding and decoding times on GPUs, unlike other DWT-based learned compression systems in the literature.