A quench arrangement for quenching glass sheets includes a main quench station having upper and lower main quench heads for performing a primary quench operation on a glass sheet, a first lower secondary quench head located downstream of the main quench station, and a second lower secondary quench head located downstream of the first lower secondary quench head. The arrangement further includes an upper secondary quench system positioned above the first and second lower secondary quench heads, and the upper secondary quench system is cooperable with the lower secondary quench heads to perform further cooling of the glass sheet. The arrangement further includes a conveyor located above the second lower secondary quench head for moving the glass sheet away from the second lower secondary quench head.