We describe two complementary techniques to aid the automatic verification of safety properties of synchronous systems by model checking. A first technique allows the automatic generation of certain inductive invariants for mode variables. Such invariants are crucial in the verification of safety properties in systems with complex modal behavior. A second technique allows the simultaneous verification of multiple properties incrementally. Specifically, the outcome of a property - valid or invalid - is communicated to the user as soon as it is known. Moreover, each property proven valid is used immediately as an invariant in the model checking procedure to aid the verification of the remaining properties. We have implemented these techniques as new options in the Kind model checker. Experimental evidence shows that these two techniques combine synergistically to increase Kind's precision as well as its speed.