A new scheme for coding both the shape and texture of arbitrarily shaped visual objects is presented. Based on set partitioning on hierarchical trees (SPIHT), the proposed Shape and Texture SPIHT (ST-SPIHT) employs a novel implementation of the shape-adaptive discrete wavelet transform (SA-DWT) using in-place lifting, along with parallel coding of texture coefficients and shape mask pixels to create a single embedded code that allows for fine-grained rate-distortion scalability. The single output code simplifies the logistics of object storage and transmission compared to previously published schemes. An input parameter provides control over the relative progression between shape and texture coding in the embedded code, allowing for adjustment of the emphasis of shape versus texture quality in low bit rate reconstructions. The combination of features provided by ST-SPIHT, namely, explicit and progressive shape coding in parallel with wavelet-based embedded coding of the object texture, is unique compared to previously published schemes. Computational complexity is minimized since the shape coding takes advantage of the decomposition and spatial orientation trees used for texture coding. Objective and subjective simulation results show that the proposed ST-SPIHT scheme has rate-distortion performance comparable or superior to MPEG-4 Visual Texture Coding for most bit rates