Clyde Rathbone and Morgan Turinui, who were part of the 59-man squad, were not considered due to injury, while second-rower Mitch Chapman will utilise his non-selection to undergo shoulder surgery.
Twenty-year-old rookie half-back Josh Holmes, who sat on the sidelines behind Valentine and Sheehan for all but two Super 14 games at the Waratahs this season, was included in the squad along with George Gregan and Sam Cordingley at number nine.
Young Reds playmaker Berrick Barnes made the cut along with Stephen Larkham and Sam Norton-Knight at fly-half - but teenagers Quade Cooper and Kurtley Beale missed out.
Adam Freier and Reds rake Stephen Moore look to have the hooking role sewn-up after Paul's non-selection, while Julian Huxley looks odds-on to take over at fullback for the injured Chris Latham.
Seven more players will be cut after a three-day training camp in Sydney this week to give the final 30-man squad for the upcoming Test series.
Wallabies head coach John Connolly claimed that many places are still up for grabs with heavy competition in the positions of prop, lock, number eight, centre and wing.
"The camp will give us a starting point in our preparation for the first Test against Wales in Sydney on May 26 and will give us the opportunity to have a closer look at a few of the players before we decide on the final squad of 30 next Sunday," said Connolly.
Most of the 22 players cut will be part of the 25-man Australia A squad for the five-match Pacific Nations Cup in May and June.
Wallabies 37-man squad for three-day Sydney training camp:
Al Baxter, Rodney Blake, Benn Robinson, Matt Dunning, Guy Shepherdson, Adam Freier, Stephen Moore, Mark Chisholm, Nathan Sharpe, Dan Vickerman, Hugh McMeniman, James Horwill, Rocky Elsom, George Smith, Phil Waugh, Stephen Hoiles, David Lyons, Wycliff Palu, Jone Tawake,
George Gregan, Sam Cordingley, Josh Holmes, Stephen Larkham, Sam Norton-Knight, Berrick Barnes, Matt Giteau, Stirling Mortlock, Adam Ashley-Cooper, Ryan Cross, Scott Staniforth, Lote Tuqiri, Mark Gerrard, Digby Ioane, Drew Mitchell, Lachlan Turner, Julian Huxley, Cameron Shepherd.