Paleotidal records obtained from sedimentary tidal rhythmites may be systematically abbreviated and so may give incorrect paleotidal and paleorotational values. The validity of determined values, including past length of day (l.o.d.), can be assessed by testing for internal self-consistency through application of the laws of celestial mechanics. Three independent values obtained from the ~620-Ma Elatina--Reynella rhythmites in South Australia (14.1 sidereal months/year, 401 sidereal days/year, and 19.5 years for the lunar nodal period), when employed in different equations that make allowance for lunar and solar tidal effects, each give a lunar semimajor axis in the range of 96.5--96.9% of the present figure. Such self-consistency strongly supports the validity of the derived l.o.d. of 21.9 hours at ~620 Ma. The validity of the estimated l.o.d. of 20.9 hours at ~900 Ma (revised value, Big Cottonwood rhythmites, Utah) and of 17.1--18.9 hours at ~2.5 Ga (Weeli Wolli rhythmites, Western Australia) cannot be assessed in that way because each data set has only one directly determined value. The derived mean rate of lunar retreat of 2.16 cm/year since ~620 Ma averts a close approach of the Moon at least since 3 Ga and a lower rate of retreat seems likely during the Proterozoic.¿ 1997 American Geophysical Union