An aspect includes providing rollback support in an exposed-pipeline processing element. A method for providing rollback support in an exposed-pipeline processing element includes detecting, by rollback support logic, an error associated with execution of an instruction in the exposed-pipeline processing element. The rollback support logic determines whether the exposed-pipeline processing element supports replay of the instruction for a predetermined number of cycles. Based on determining that the exposed-pipeline processing element supports replay of the instruction, a rollback action is performed in the exposed-pipeline processing element to attempt recovery from the error.