Innovations in compression and decompression of point cloud data are described. For example, an encoder is configured to encode point cloud data, thereby producing encoded data. In particular, the encoder applies a region-adaptive hierarchical transform (“RAHT”) to attributes of occupied points, thereby producing transform coefficients. The encoder can also quantize the transform coefficients and perform adaptive entropy coding of the quantized transform coefficients. For corresponding decoding, a decoder is configured to decode the encoded data to reconstruct point cloud data. In particular, the decoder applies an inverse RAHT to transform coefficients for attributes of occupied points. The decoder can also perform adaptive entropy decoding and inverse quantization of the quantized transform coefficients. The adaptive entropy coding/decoding can use estimates of the distribution of values for the quantized transform coefficients. In this case, the encoder calculates the estimates and signals them to the decoder.