  A method of transmitting information in interstellar space at superluminal,
or $> c$, speeds is proposed. The information is encoded as phase modulation of
an electromagnetic wave of constant intensity, i.e. fluctuations in the rate of
energy transport plays no role in the communication, and no energy is
transported at speed $>$ c. Of course, such a constant wave can ultimately last
only the duration of its enveloping wave packet. However, as a unique feature
of this paper, we assume the source is sufficiently steady to be capable of
emitting wave packets, or pulses, of size much larger than the separation
between sender and receiver. Therefore, if a pre-existing and enduring wave
envelope already connects the two sides, the subluminal nature of the
envelope's group velocity will no longer slow down the communication, which is
now limited by the speed at which information encoded as phase modulation
propagates through the plasma, i.e. the phase velocity $v_p > c$. The method
involves no sharp structure in either time or frequency. As a working example,
we considered two spaceships separated by 1 lt-s in the local hot bubble.
Provided the bandwidth of the extra Fourier modes generated by the phase
modulation is much smaller than the carrier wave frequency, the radio
communication of a message, encoded as a specific alignment between the carrier
wave phase and the anomalous (modulated) phase, can take place at a speed in
excess of light by a few parts in 10$^{11}$ at $\nu\approx 1$~GHz, and higher
at smaller $\nu$.
