There are described methods and systems for operating an aircraft turboprop engine. The method comprises controlling a propeller of the turboprop engine based on a selected one of a reference propeller rotational speed and a minimum propeller blade angle while the turboprop engine is running; detecting an inflight restart of the turboprop engine; and controlling the propeller during the inflight restart in accordance with at least one of a modified reference propeller rotational speed and a modified minimum propeller blade angle to maintain an actual propeller blade angle above an aerodynamic disking angle during the inflight restart.