  We report on several pointed Rossi X-ray Timing Explorer observations of the
enigmatic low-mass X-ray binary (LMXB) 4U 1957+11 at different X-ray
luminosities. The luminosity of the source varied by more than a factor of four
on time scales of months to years. The spectrum of the source tends to get
harder when its luminosity increases. Only very weak (1%-2% rms amplitude;
0.001-10 Hz; 2-60 keV) rapid X-ray variability was observed during the
observations. A comparison of the spectral and temporal behaviour of 4U1957+11
with other X-ray binary systems, in particular LMC X-3, indicates that 4U
1957+11 is likely to be a persistent LMXB harboring a black hole and which is
persistently in the black-hole high state. If confirmed, it would be the only
such system known.
