The invention relates to a process air dehumidification system (2) comprising a process air dehumidifier unit (4) comprising a moisture absorbing agent (6), the process air dehumidification system (2) further comprising a moisture absorbing agent regeneration system (8) comprising a closed regeneration air loop (10) arranged to pass through the process air dehumidifier unit (4) and comprising regeneration air flow generating means (12) for generating a regeneration air flow (14) in the closed regeneration air loop (10) and comprising a heat pump (16) comprising a condenser (18) and an evaporator (20) and a heat pump refrigerant (22), where the closed regeneration air loop (10) is arranged to pass through the condenser (18) and the evaporator (20) to exchange heat between regeneration air (24) and heat pump refrigerant (22), where the dehumidification system (2) comprises a complementary regeneration air moisture removal system (26) arranged downstreams of the evaporator (20) and upstreams of the condenser (18) and a regeneration air heat bypass system (28) arranged to exchange heat from inlet regeneration air (30) upstreams of the dehumidifier unit (4) and downstreams of the condenser (18) to outlet regeneration air (32) downstreams of the dehumidifier unit (4) and upstreams of the evaporator (20) and means (34) arranged to activate and deactivate the complementary regeneration air moisture removal system (26) and the regeneration air heat bypass system (28). The invention also relates to a method for dehumidification of process air.