A mutant prourokinase plasminogen activator (M5) was developed to make prouPA less subject to spontaneous activation during fibrinolysis. C1-inhibitor complexes with tcM5. The effect of C1-inhibitor on fibrinolysis and fibrinogenolysis by M5 was determined. Supplemental C1-inhibitor restores the stability of M5 but not that of prouPA. Clot lysis by M5 with supplemental C1-inhibitor showed no attenuation of the rate of fibrinolysis, whereas fibrinogenolysis was prevented by C1-inhibitor. Due to higher dose tolerance of M5 with C1-inhibitor, the rate of fibrin-specific lysis reached that achievable by nonspecific fibrinolysis without inhibitor. Plasma C1-inhibitor stabilized M5 in plasma by inhibiting tcM5 and thereby non-specific plasminogen activation. At the same time, fibrin-specific plasminogen activation remained unimpaired. This unusual dissociation of effects has significant implications for improving the safety and efficacy of fibrinolysis. Methods of reducing bleeding and non-specific plasminogen activation during fibrinolysis by administering M5 along with exogenous C1-inhibitor are disclosed.