When two small viscous drops are sufficiently close, van der Waals force overcomes surface tension and deforms the surfaces into contact, initiating coalescence. The dynamics of surface deformation across an inviscid gap are self-similar as contact is approached, with both radial and gap scales varying as t^{'1/3} for time until contact t^{'}. Van der Waals and viscous forces are dominant. The self-similar profiles are both nonuniversal and of the second kind: the observed t^{'1/3} behavior is selected only by the subdominant surface tension.