An insufflator for minimally invasive surgery, containing a) a gas connection having a pressure and flow rate control unit equipped with a proportional valve and a pressure sensor, b) a supply line having an optional filter und connection to a first trocar, c) a second trocar having a tube and optional filter, connected to a suction device having an adjustable suction power, d) an electronic or mechanical control unit, e) a device for determining the suction flow rate, the device for determining the suction flow rate being realized in the form of a flow rate measurement unit or by determining the power of the suction pump, the control unit being designed to control the suction power of the waste gas suction by the following steps, as required: a. a fixed maximum insufflation flow rate q max is determined by defining the maximum pressure and taking into account the flow resistance of the used trocar/instrument combination, and a maximum exchange flow rate ( q suction,max + q leakage < q exchange,max) is set, b. determining the current leakage flow rate q leakage by a mathematical model, c. calculating the maximum possible suction flow rate q suction,max: by subtracting the determined leakage from the maximum insufflation flow rate q max and subsequently multiplying the result by a safety factor of between 0.6 and 0.9, d. cyclically checking whether the suction flow rate plus the estimated leakage is smaller than the set maximum exchange flow rate q suction,max e. if the condition ( q suction,max + q leakage < q exchange,max) is met, the suction flow rate q suction,max of the pump is adjusted, if the condition is not met, the suction flow rate q suction,max is reduced to such an extent that the condition is met, if q suction,max cannot be further reduced, a zero value is selected for q suction,max f. cyclically repeating the steps in order to adapt to leakage changes or changes to the trocar/instrument combination. a) a gas connection having a pressure and flow rate control unit equipped with a proportional valve and a pressure sensor, b) a supply line having an optional filter und connection to a first trocar, c) a second trocar having a tube and optional filter, connected to a suction device having an adjustable suction power, d) an electronic or mechanical control unit, e) a device for determining the suction flow rate, the device for determining the suction flow rate being realized in the form of a flow rate measurement unit or by determining the power of the suction pump, the control unit being designed to control the suction power of the waste gas suction by the following steps, as required: a. a fixed maximum insufflation flow rate q max is determined by defining the maximum pressure and taking into account the flow resistance of the used trocar/instrument combination, and a maximum exchange flow rate ( q suction,max + q leakage < q exchange,max) is set, b. determining the current leakage flow rate q leakage by a mathematical model, c. calculating the maximum possible suction flow rate q suction,max: by subtracting the determined leakage from the maximum insufflation flow rate q max and subsequently multiplying the result by a safety factor of between 0.6 and 0.9, d. cyclically checking whether the suction flow rate plus the estimated leakage is smaller than the set maximum exchange flow rate q suction,max e. if the condition ( q suction,max + q leakage < q exchange,max) is met, the suction flow rate q suction,max of the pump is adjusted, if the condition is not met, the suction flow rate q suction,max is reduced to such an extent that the condition is met, if q suction,max cannot be further reduced, a zero value is selected for q suction,max f. cyclically repeating the steps in order to adapt to leakage changes or changes to the trocar/instrument combination. a. a fixed maximum insufflation flow rate q max is determined by defining the maximum pressure and taking into account the flow resistance of the used trocar/instrument combination, and a maximum exchange flow rate ( q suction,max + q leakage < q exchange,max) is set, b. determining the current leakage flow rate q leakage by a mathematical model, c. calculating the maximum possible suction flow rate q suction,max: by subtracting the determined leakage from the maximum insufflation flow rate q max and subsequently multiplying the result by a safety factor of between 0.6 and 0.9, d. cyclically checking whether the suction flow rate plus the estimated leakage is smaller than the set maximum exchange flow rate q suction,max e. if the condition ( q suction,max + q leakage < q exchange,max) is met, the suction flow rate q suction,max of the pump is adjusted, if the condition is not met, the suction flow rate q suction,max is reduced to such an extent that the condition is met, if q suction,max cannot be further reduced, a zero value is selected for q suction,max if the condition is not met, the suction flow rate q suction,max is reduced to such an extent that the condition is met, if q suction,max cannot be further reduced, a zero value is selected for q suction,max f. cyclically repeating the steps in order to adapt to leakage changes or changes to the trocar/instrument combination.