We consider a simple method to improve the adaptiveness and flexibility of bit-interleaved coded modulation (BICM) for various channel models. With state-of-the art adaptive transmission techniques, the raw adaptation of the data rate to the channel characteristics is usually done by selecting an appropriate signal constellation and the fine adaptation is done by changing the code rate. To enable a fine adaptation also with the modulation, irregular modulation schemes have been introduced in [1]. With irregular modulation, different signal constellations may be used within one code block, even if only the average channel state is known at the transmitter. In this paper, irregular modulation schemes are analyzed using EXIT charts, capacity, error bounds and error rate simulations.