A well system can include an accumulator in communication with a wellbore, whereby the accumulator applies pressure to the wellbore. A method of maintaining a desired pressure in a wellbore can include applying pressure to the wellbore from an accumulator in response to pressure in the wellbore being less than the desired pressure. Another well system can include a dampener in communication with a wellbore isolated from atmosphere, whereby the dampener mitigates pressure spikes in the wellbore.