In 2008, Rodshtein was a member of the Israeli team in the 38th Chess Olympiad in Dresden; he scored 7 points from 9 games, contributing to the team silver medal. In particular, he was responsible for Israel's win against the Olympic champion, Armenia. A few months later he was offered by Armenia's No. 1 Levon Aronian to work with him as a second. Rodshtein shared 1st in the 2008 Israeli championship, but didn't retain the title due to inferior tie-break. In 2010 he took clear first place in the 12th International Open of Sants, Hostafrancs and La Bordeta in Barcelona. In 2011 Rodshtein tied for 4th–10th with Rustam Kasimdzhanov, Gata Kamsky, Rauf Mamedov, Ivan Cheparinov, Denis Khismatullin and Yu Yangyi in the Aeroflot Open in Moscow. In the same tournament in 2012, he tied for 4th–8th with Alexander Khalifman, Hrant Melkumyan, Fabiano Caruana and Dmitry Andreikin. Rodshtein tied for first with Sanan Sjugirov, Parimarjan Negi, Vlad-Cristian Jianu, Sergey Fedorchuk, Eric Hansen, Alexei Fedorov, and Yuri Vovk, finishing third on tiebreak, at the 2013 Cappelle-la-Grande Open. He won the 45th Rilton Cup, which took place from 27 December 2015 to 5 January 2016 in Stockholm, with a score of 8/9 points.