Components of the neutron energy spectrum measured by instruments on the Lunar Prospector (LP) spacecraft have been optimistically interpreted as indicating massive deposits of water ice or other hydrogenic minerals in the polar regions of the Moon. An independent reanalysis of the theory of leakage neutrons shows that in addition to the observed depressions of the epithermal neutron flux the signature of polar hydrogen in the lunar regolith would have included a distinctive increase in the thermal neutron flux that apparently was not detected. Other simulations of LP neutron data show that the neutron signature of a mineralogical anomaly as simple as a localized excess of silicate would be about the same as that of hydrogen. A deficit of CaO would produce the LP result, that is, a decrease of epithermal neutrons with no noticeable change in the thermal neutron flux. Other more complicated mineral variants could yield similar effects. What is clear is that the existence of polar water ice or hydride deposits has not been proven by analyses of Lunar Prospector data.