Over the weekend I had a closer look at the possibilities of reducing the
bandwidth of a BPSk signal by continuous phase modulation.
Simple simulations show that the bandwidth of the signal is reduced when
continuous phase modulation is applied. When 5% of the bit-time (= 5ms) is
allowed the continuous phase shift the bandwidth of the BPSK signal should
be less than that of a normal keyed CW transmission at 12WPM.
Next question was how to implement the continuous phase shift?
One way would be to implement this digital, but this would require a rather
high reference oscillator (in the 30-100MHz range, depending on how 'soft'
the signal should be).
But there might be an alternative and much simpler way :
If you send an RF signal through a (resonant) LC-circuit this circuit will
act as a kind of 'freewheel' where any change of amplitude ... and phase
will be 'softened'. So if one would send a 'rude BPSK' signal (as is
created with an XOR gate) through a resonant LC-circuit you will get
continuous phase shift at the output. The phase shift time will depend on
the Q of the LC-circuit, for our purposes (+/- 5ms phase shift time) we
would need a Q of about 700. At 136kHz it should not be impossible to
achieve such a Q, especially if we not use a simple passive LC circuit but
a LC-circuit with feedback amplifier.
A side effect will be that there is also some AM created, but this can be
'corrected' by an AGC amplifier (or just hard clipping, but this might
increase bandwidth too much).
A main advantage would be that the whole BPSK modulation circuitery can be
inserted between VFO and PA.

73, Rik  ON7YD