A lightmap question

I finished a radiosity lighting algorithim a while ago that created lightmaps for quads. It was used in a level editor that I recently converted to use triangles instead of quads, and thus I have a few questions on changing the algorithim to facilitate the ability to compute lightmaps for triangles. Textures are square (more or less) but triangles are, well, triangular. If I want each triangle to have its own lightmap, do i need to waste half of the lightmap texture because it is never visible? Seems like a waste of memory, but maybee it isnt that big of a hit if my textures are at most 16x16 on really big triangles which rarely occur. If you have any other advice, do tell. Thanks.