  As part of a large-scale search for coherent pulsations from LMXBs in the
RXTE archive, we have completed a detailed series of searches for coherent
pulsations of 4U 1820-30 -- an ultracompact LMXB with a binary period of 11.4
minutes located in the globular cluster NGC6624. The small binary period leads
to a very high acceleration, so we used phase modulation searches as well as
acceleration searches to give significant sensitivity to millisecond
pulsations. We searched a total of 34 archival RXTE observations, 32 of which
had an on-source integration time longer than 10 ks, and some of which were
made consecutively which allowed us to combine them. While we found no
pulsations, we have been able to place the first stringent (95% confidence)
pulsed fraction limits of < 0.8% for all realistic spin frequencies (i.e. < 1
kHz) and likely companion masses (0.02 Msun < Mc < 0.3 Msun). By contrast all
five LMXBs known to emit coherent pulsations have intrinsic pulsed fractions in
the range 3% to 7% when pulsations are observed.
