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This paper presents a very low-memory wavelet compression architecture for implementation in severely constrained hardware environments such as wireless sensor networks (WSNs). The approach employs a strip-based processing technique where an image is partitioned into strips and each strip is encoded separately. To further reduce the memory requirements, the wavelet compression uses a modified set-partitioning in hierarchical trees (SPIHT) algorithm based on a degree-0 zerotree coding scheme to give high compression performance without the need for adaptive arithmetic coding which would require additional storage for multiple coding tables. A new one-dimension (1D) addressing method is proposed to store the wavelet coefficients into the strip buffer for ease of coding. A softcore microprocessor-based hardware implementation on a field programmable gate array (FPGA) is presented for verifying the strip-based wavelet compression architecture and software simulations are presented to verify the performance of the degree-0 zerotree coding scheme.