Measurements on current quantum processors are subject to hardware imperfections that lead to readout errors. These errors manifest themselves as a bias in quantum expectation values. Here, we consider a very simple method that forces the bias in the expectation value to appear as a multiplicative factor that can be measured directly and removed at the cost of an increase in the sampling complexity for the observable. This method was previously discussed by Karalekas et al. [Quantum Sci. Technol. 5, 024003 (2020)2058-956510.1088/2058-9565/ab7559] for the product of single-qubit readout-error models. Here, we formally analyze the method and show that it can be applied to general noise models. In particular, we show the method does not need to assume any specific form of the noise model and requires only that the noise is "weak"to avoid excessive sampling overhead. We prove bounds relating the error in the expectation value to the sample complexity.