The performance of directly-modulated lasers (DMLs) is severely impaired by nonlinear behaviour when operating at high symbol rates. We propose a new linearization method for DML-based transmitters which can significantly reduce nonlinearity. This method, named the Stretched A (StrA) method, relies on the generation of an approximation to the ideal modulating current that generates a linear optical output waveform. In Part I of this work, the theoretical framework of the proposed method is presented and detailed simulation studies illustrate its implementation and demonstrate the benefits it offers. Although the method is applicable to any type of DML, the simulation studies presented herein focus on optical links based on vertical-cavity surface-emitting lasers (VCSELs) as these comprise the vast majority of short-reach optical links. Part II of this work presents the proof-of-principle experimental demonstration of this new linearization method and discusses its possible implementations using either analog or digital electronics.