If you have a supertweeter crossed too low (like 15kHz) it will interfere with your main tweeter with unpredictable results. Remember that at 15kHz, the wavelength of sound is in the order of a few millimeters, so if you place your supertweeter off by a fraction of an mm, the interference pattern will be different. The high frequencies may be either enhanced or destroyed ... depending on the summation of waves by the time it reaches your ear.
You may or may not like the sound this interference, but of course that is up to you :)
You may or may not like the sound this interference, but of course that is up to you :)