Although skeptical of the prohibitive power of no-hidden-variables the
orems, John Bell was himself responsible for the two most important on
es. I describe some recent versions of the lesser known of the two (fa
miliar to experts as the ''Kochen-Specker theorem'') which have transp
arently simple proofs. One of the new versions can be converted withou
t additional analysis into a powerful form of the very much better kno
wn ''Bell's Theorem,'' thereby clarifying the conceptual link between
these two results of Bell.