It is well known that ageing and noise exposure are important causes of sensorineural hearing loss, and can result in damage of the outer hair cells or other structures of the inner ear, including synaptic damage to the auditory nerve (AN), i.e., cochlear synaptopathy (CS). Despite the suspected high prevalence of CS among people with self-reported hearing difficulties but seemingly normal hearing, conventional hearing-aid algorithms do not compensate for the functional deficits associated with CS. Here, we present and evaluate a number of auditory signal-processing strategies designed to maximally restore AN coding for listeners with CS pathologies. We evaluated our algorithms in subjects with and without suspected age-related CS to assess whether physiological and behavioural markers associated with CS can be improved. Our data show that after applying our algorithms, envelope-following responses and perceptual amplitude-modulation sensitivity were consistently enhanced in both young and older listeners. Speech intelligibility showed small improvements across participants, with the young group benefitting the most from processed speech. Our proposed hearing-restoration algorithms can be rapidly executed and can thus extend the application range of current hearing aids and hearables, while leaving sound amplification unaffected.