The strong toroidal magnetic field required for plasma confinement in tokamaks is generated by a set of D-shaped coils lying equidistant on meridian planes toroidally located around the central axis of the device. A major technological challenge tied to this configuration is represented by the large Lorentz force acting on the coils and arising from the interaction of the coils' currents with the magnetic field generated by the coil system itself. As this force is given by the cross product of the coil current and the magnetic field, various kinds of coil geometry modification have been proposed to alleviate this problem, from an inclination of the entire coil in order to maintain its planarity, to azimuthal tilting of all, or parts of, the coil profile. When the inner legs of the coils are tilted, apart from a reduction of the electromagnetic forces, a solenoid-like structure is formed which introduces additional magnetic flux linked to the plasma. Considering compact, high field devices, it is shown that when this additional flux is exploited, totally or in part, to ramp up the plasma current, the discharge time can be extended by a significant amount without resorting to noninductive current drive systems. Operational scenarios with inner-leg-tilted toroidal field coils are presented.