A method of safe pressurized mud cap drilling comprising: determining a set point for a surface backpressure choke manifold; injecting sacrificial fluids into a drillstring disposed in a wellbore; injecting weighted mud into an annulus surrounding the drillstring, wherein the annulus is sealed and wherein one or more pumps for injecting weighted mud are turned on and left on at a substantially constant flow rate during safe pressurized mud cap drilling; and controlling an effective injection rate of weighted mud into the annulus by: monitoring a surface backpressure, if the surface backpressure rises above the set point, closing one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to increase the effective injection rate of weighted mud into the annulus, if the surface backpressure falls below the set point, opening the one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to decrease the effective injection rate of weighted mud into the annulus, and if the surface backpressure is substantially equal to the set point, maintaining a state of the one or more chokes of the surface backpressure choke manifold to maintain the effective injection rate of weighted muds into the annulus. determining a set point for a surface backpressure choke manifold; injecting sacrificial fluids into a drillstring disposed in a wellbore; injecting weighted mud into an annulus surrounding the drillstring, wherein the annulus is sealed and wherein one or more pumps for injecting weighted mud are turned on and left on at a substantially constant flow rate during safe pressurized mud cap drilling; and controlling an effective injection rate of weighted mud into the annulus by: monitoring a surface backpressure, if the surface backpressure rises above the set point, closing one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to increase the effective injection rate of weighted mud into the annulus, if the surface backpressure falls below the set point, opening the one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to decrease the effective injection rate of weighted mud into the annulus, and if the surface backpressure is substantially equal to the set point, maintaining a state of the one or more chokes of the surface backpressure choke manifold to maintain the effective injection rate of weighted muds into the annulus. monitoring a surface backpressure, if the surface backpressure rises above the set point, closing one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to increase the effective injection rate of weighted mud into the annulus, if the surface backpressure falls below the set point, opening the one or more chokes of the surface backpressure choke manifold in a stepwise incremental manner to decrease the effective injection rate of weighted mud into the annulus, and if the surface backpressure is substantially equal to the set point, maintaining a state of the one or more chokes of the surface backpressure choke manifold to maintain the effective injection rate of weighted muds into the annulus.