Cognitive radio technology enables two wireless networks, namely a primary network and a secondary network, to operate in the same geographic region sharing the same spectrum. Primary users have priority to access the spectrum without taking into account the presence of secondary users, while secondary users have to limit their interference in order not to disturb the operation of primary users. This work analyses a cognitive network in which the secondary network can adapt its parameters, in order to exploit any available opportunity for secondary capacity improvement, under the restriction that these adjustments cannot cause any additional harm to primary users. Using Poisson point process modelling, the authors present a closed-form formulation to adjust the secondary modulation order, user density, and transmit power, in order to maximise the secondary capacity, without causing any additional disturbance to primary users, and keeping the quality of secondary transmissions above a minimum acceptable level. The formulation proposed allows us to gain meaningful insights regarding the interrelationship involving some network parameters and performance metrics.