  We present two variants of Wythoff's game. The first game is a restriction of
Wythoff's game in which removing tokens from the smaller pile is not allowed if
the two entries are not equal. The second game is an extension of Wythoff's
game obtained by adjoining a move allowing players to remove k tokens from the
smaller pile and l tokens from the other pile provided l < k. We show that both
games preserve the P-positions of Wythoff's game. This resolves a question
raised by Duchene, Fraenkel, Nowakowski and Rigo. We give formulas for those
positions which have Sprague-Grundy value 1. We also prove several results on
the Sprague-Grundy functions.
