I have a relatively old graphics card, but when I query about the extensions it supports, it returns GL_EXT_point_parameters among other extensions, but when I try to use this extensions it doesn’t work like it’s supposed to. Is there anything that enables or disables this extention? What could I have missed?

Just a guess…you have a Savage4? It doesn’t work on my Savage4, though it is listed as a supported extension.

No. It’s not Savage4. It’s from ASUS, an AGP-V3000ZXTV, with RIVA chip. Well, I managed to get it partially working. The size of the point changes when its depth changes, but its Alpha color component, doesn’t change.

Have you enabled blending?

Yes, blending is enabled. The blending function is set to GL_SRC_ALPHA, for source fragments, and GL_ONE_MINUS_SRC_ALPHA, for destination fragments. In addition, I tried it with both GL_POINT_SMOOTH enabled and disabled.