Jesse Levine caused one of the upsets of the tournament with a four-set win over 14th seed Marat Safin, who announced his retirement from the game after the match.
Third seed Andy Murray is a possible opponent for Levine who overcame a clear height disadvantage to win 6-2, 3-6, 7-6, 6-4.
Wayne Odesnik suffered another painful exit from Wimbledon on Tuesday.
He was comfortably beaten by Jurgen Meltzer 6-1, 6-4, 6-2. South African born Odesnik was hampered by a groin strain and was forced to call a trainer on to the court.
He said: “It was the same injury as last year but I am not using it as an excuse as Jurgen is a good grass court player. He deserved to win.”
Having failed to bypass the first round at Wimbledon, Odesnik spoke of his admiration for the event. “Wimbledon is awesome,” he said. “It’s a great experience to play.”
Top Israelis Dudi Sela and Shahar Peer are in round two action on Wednesday. Sela tackles 18th seed Schuettler of Germany in the first game on Court 12. Peer takes on Nicole Petrova (10) on Court 14.