Modern image coders balance bitrate used for encoding the location of signicant transform coefficients, and bitrate used for coding their values. The importance of balancing location and value information in practical coders raises fundamental open questions about how to code even simple processes with joint uncertainty in coefficient location and magnitude. This paper studies the most basic example of such a process: a 2-D process studied earlier by Weidmann and Vetterli that combines Gaussian magnitude information with Bernoulli location uncertainty. The paper offers insight into the coding of this process by investigating several new coding strategies based on more general approaches to lossy compression of location. Extending these ideas to practical coding, we develop a trellis-coded quantization algorithm with performance matching the published theoretical bounds. Finally, we evaluate the quality of our strategies by deriving a rate-distortion bound using Blahut's algorithm for discrete sources.