The robustness of automatic speech recognition systems to noise is still a problem, especially for small footprint systems. This paper addresses the problem of noise robustness using model compensation methods. Such algorithms are already available, but their complexity is usually high. An often-referenced method for achieving noise robustness is parallel model combination (PMC). Several algorithms have been proposed to develop more computationally efficient methods than PMC. For example, Jacobian adaptation approximates PMC with a linear transformation function in the cepstral domain. However, the Jacobian approximation is valid only for test environments that are close to the training conditions whereas, in real test conditions, the mismatch between the test and training environments is usually large. In this paper, we propose two methods, respectively called static and dynamic α-Jacobian adaptation (or α-JAC), to compute new linear approximations of PMC for realistic test environments. We further extend both algorithms to compensate for additive and convolutional noise and we derive the corresponding non-linear algorithm that is approximated. All these algorithms are experimentally compared in important mismatch conditions. As compared to Jacobian adaptation, improvements are observed with both static and dynamic α-Jacobian adaptation. [Copyright &y& Elsevier]