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Racing Kings, http://www.chessvariants.org/diffobjective.dir/racing.html,
is Pawnless.  Betza's Feeble Chess right below has the weakest Rook equal to 0.2 of a Pawn, so weak pieces and Pawns can and do overlap and coincide in ''Pawn'' just being a convenient lower-value piece. Pawnless Ecumenical, 
http://www.chessvariants.org/large.dir/ecumenical-chess.html, is one of several by Gilman that work.  Bruck's nails down the name Pawnless, 
http://www.chessvariants.org/44.dir/pawnless.html.  Each Pawn is different here: http://www.chessvariants.org/diffmove.dir/pawnschess.html. The latter raises the question, is the standard western Pawn the best one possible? Shatranj Pawn is about 1/4 of a Knight. Perfected Modern OrthoPawn is 1/3 of a Knight. The enhancements are the two-step option and stronger promotion opportunity.
Sergeant, http://www.chessvariants.org/piececlopedia.dir/sergeant.html, is revisited by Hutnik as Pawns-X-Forward or Eurasian, without Sergeant's move-only diagonal, for where rows number 9 or 11, thus allowing mutual unattacking two(three)-steps and one clear central rank but strengthened Pawn for the larger boards.