Background: Individuals with acquired phonological dyslexia experience difficulty associating written letters with corresponding sounds, especially in pseudowords. Previous studies have shown that reading can be improved in these individuals by training letter-sound correspondence, practicing phonological skills, or using combined approaches. However, generalisation to untrained items is typically limited. Aims: We investigated whether principles of phonological complexity can be applied to training letter-sound correspondence reading in acquired phonological dyslexia to improve generalisation to untrained words. Based on previous work in other linguistic domains, we hypothesised that training phonologically "more complex" material (i.e., consonant clusters with small sonority differences) would result in generalisation to phonologically "less complex" material (i.e., consonant clusters with larger sonority differences), but this generalisation pattern would not be demonstrated when training the "less complex" material. Methods & Procedures: We used a single-participant, multiple baseline design across participants and behaviours to examine phonological complexity as a training variable in five individuals. Based on participants' error data from a previous experiment, a "more complex" onset and a "less complex" onset were selected for training for each participant. Training order assignment was pseudo-randomised and counterbalanced across participants. Three participants were trained in the "more complex" condition and two in the "less complex" condition while tracking oral reading accuracy of both onsets. Outcomes & Results: As predicted, participants trained in the "more complex" condition demonstrated improved pseudoword reading of the trained cluster and generalisation to pseudowords with the untrained, "simple" onset, but not vice versa. Conclusions: These findings suggest phonological complexity can be used to improve generalisation to untrained phonologically related words in acquired phonological dyslexia. These findings also provide preliminary support for using phonological complexity theory as a tool for designing more effective and efficient reading treatments for acquired dyslexia.