Here is the on-axis response for the Radio Shack LX550 loudspeaker, which combines a 5" kevlar woofer with the Linaeum dipole tweeter. The lack of output above 9 kHz is due to an on-axis null in the radiation pattern of the tweeter. In addition, the very short tone burst measurement method used does not capture the full contribution of the tweeter's back wave. Still -- the LX550 definitely lacks sparkle when listened to on-axis.
Here is the response 30 degrees off axis. The highs are back up to reference level, but a null develops lower down.
This Project suggests modification to the crossover (well -- a whole new crossover) that provides a more extended, detailed sound. Interestingly, the revised crossover measures very similarly on axis to the stock unit. The improvement comes from getting the woofer out of the way of the tweeter and allowing most of the output above 3 kHz to come from the superior tweeter.