Within two weeks of combat against the Soviet Air Force, Bär's tally rose to 27, which earned him the Knight's Cross of the Iron Cross on 2 July, followed by his promotion to "Oberleutnant" on 1 August 1941. On 5 July, Bär or Mölders may also have shot down the Soviet fighter ace "Podpolkovnik" (Lieutenant Colonel) Stepan Suprun from the 401 IAP ("Istrebitel'nyy Aviatsionyy Polk"—fighter aviation regiment) and holder of the Hero of the Soviet Union. Bär accounted for a Petlyakov Pe-2 on 23 July. Three were lost from the 411 BAP ("Bombardirovochnyy Aviatsionyy Polk"—bomber aviation regiment) operating under the OSNAZ ("Osoboye Naznachenie"—Special purpose-unit or task force). German pilots submitted three claims. On 9 August an SB bomber was claimed from a formation of eight belonging to the 57 BAP's 3rd "Eskadrilya"—five Soviet aircraft were shot down. Bär had achieved his 55th victory.