By restricting the color palette to 16 bit means, I think, that you simply don't get a full palette grayscale alpha channel. 16 bit and 24 bit color have the same number of colors, except that in 24 bit you get a grayscale alpha channel (the extra 8 bits), as opposed to the 1 bit alpha channel of the 16 bit specification.
So, you can still use transparency, but it has to be 1 bit, hard-edge transparency as in a GIF, not soft-edge transparency like a PNG-24 (24-bit, 16 bit + 8 bit alpha channel.)
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