Add a layer mask, then color it either black (No shine) or a dark shade of gray, then apply it. This should change the alpha channel reducing the shine.
Took me years to find this out after people telling me nothing but "change the alpha", so hope it helps.
Specifically, in Gimp, when you "Add Layer Mask", you need to choose the option "Transfer the layer's alpha channel". Otherwise when you apply the layer mask, the transparency change will stick but the alpha channel will remain white, so your object will still be shiny in-game.
How about save the texture as a DXT1 WITHOUT alpha?
Stop suggesting to WASTE an entire 8bit texture channel with a black texture. This doubles the texture sfile size, and you are flood filling it with black.
Just ditch the spec map entirely if you are not making a [censored] spec map.
just use the material property spec level to adjust global spec levels on objects.
What he means to say is that if you don't actually need the object to be shiny at all, it is more efficient to skip all this alpha channel hullabaloo, and save your normal map with DXT-1 compression. Because DXT-1 ignores the alpha channel, your object will not have any shine, just as though the alpha channel was completely black.