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Continuous phase modulation (CPM) is widely employed in digital communication systems due to its high spectral efficiency. The main digital implementations originate in the well-known ROM-based approach. In this approach, the memory size may be very large and depends completely on the modulation parameters. This means that supporting several modulation types would require a proportional increase on the memory resources. In this paper, a new versatile single $h$ and multi- $h$ CPM transmitter is introduced, which can be reconfigured for handling any kind of CPM waveform without noticeable increase in memory. A complete digital architecture is also provided. This represents a truly reconfigurable CPM transmitter, which can be used for software defined radio platforms. Implementation results show that in data rates of more than 20 Mbps as required by the IRIG-106-15 standard, the proposed approach yields a savings of around 1.5 megabits of memory when compared to the ROM approach, at the expense of requiring 15 multipliers. Additionally, for medium-rate implementations as required in the Bluetooth standard, the proposed transmitter offers a savings of about 50 Kbits of memory while requiring only two multipliers. Simulation results confirm that the signals produced by this new approach match those expected from theoretical analysis. [ABSTRACT FROM AUTHOR]