The ultrafast internal conversion and isomerization dynamics of nonadiabatic cis --> trans photoreactions are studied. The isomerizing molecule is described by a two-mode two-state model, which involves either an avoided crossing (AC) or a conical intersection (Cl, the 'funnel') of the potential-energy surfaces. To account for the localization in the cis and trans configuration due to vibrational cooling of the photoproducts, the system is coupled to a harmonic bath via Redfield theory. Although the two models are - except for the topology of the crossing surface - identical, the Cl model isomerizes about an order of magnitude faster than the AC model. This high reaction speed and efficiency of the photochemical funnel is caused by a subtle interplay of the highly localized nonadiabatic coupling of the Cl and the dissipative dynamics of the molecular system. (C) 2003 Elsevier B.V. All rights reserved.