We report the discovery of four isolated millisecond pulsars found as part of the Parkes 436 MHz survey of the southern sky. Three of the pulsars, PSRs J1024-0719, J1744-1134, and J2124-3358, are close to the Sun (d <360 pc) and have very low luminosities, ≲0.5 mJy kpc2. The other, PSR J0711-6830, is of intermediate luminosity. The four least luminous millisecond pulsars presently known are all isolated objects, even though more than 75% of the known disk millisecond pulsars are binary. A Kolmogorov-Smirnov analysis confirms that the luminosity distributions of the binary and isolated millisecond pulsars are different at the 99.5% confidence level. We can find no simple explanation for this fact. The low-luminosity millisecond pulsars reported here exacerbate the birthrate discrepancy with their assumed progenitors, the low-mass X-ray binaries. None of the pulsars exhibits any evidence of a planetary system such as that observed around PSR B1257 + 12, indicating that planetary formation around millisecond pulsars is rare. © 1997. The American Astronomical Society. All rights reserved.