In this paper we discuss the motivation, design, and analysis of ambisonic decoders for systems where the vertical order is less than the horizontal order, known as mixed-order Ambisonic systems. This can be due to the use of microphone arrays that emphasize horizontal spatial resolution or speaker arrays that provide sparser coverage vertically. First, we review Ambisonic reproduction criteria, as defined by Gerzon, and summarize recent results on the relative perceptual importance of the various criteria. Then we show that using full-order decoders with mixed-order program material results in poorer performance than with a properly designed mixed-order decoder. We then introduce a new implementation of a decoder optimizer that draws upon techniques from machine learning for quick and robust convergence, discuss the construction of the objective function, and apply it to the problem of designing two-band decoders for mixed-order signal sets and non-uniform loudspeaker layouts. Results of informal listening tests are summarized and future directions discussed.