This article studies the strategic withholding of physical transmission rights (PTRs) held by power producers in two different markets. Contrary to many previous studies, we assume that local markets are efficient but not the use of the interconnection. We model a two-settlement market, solved by backward induction. Our sensitivity analysis with respect to the allocation of PTRs brings insights on the strategic use of interconnections. Our main result is that PTR's withholding is an equilibrium strategy under quite soft conditions. This is an important consideration given the development of high-voltage direct current (HVDC) transmission lines to connect different markets.