In scenarios where gluinos and right-handed down-type squarks are relativel
y light, motivated, for example, by the SO(10) D terms,jets + is not an ele
ment of (T) signals can be observed at the luminosity-upgraded Tevatron, ev
en if the remaining squarks are very heavy. Most spectacular signals are ex
pected if the right-handed down-type squarks are lighter than the gluino. I
n the conventional MSUGRA model with very heavy squarks and the gluino mass
, consistent with the LEP bound, on the common gaugino mass, practically no
signal is expected in this channel. The possibility of distinguishing betw
een various SUGRA-motivated scenarios by exploiting the is not an element o
f (T) and the jet P-T distributions, opposite sign dileptons +jets+ is not
an element of (T) events and clean trilepton signals have been discussed.