Listeners vary in their ability to understand speech in noisy environments. Hearing sensitivity, as measured by pure-tone audiometry, can only partly explain these results, and cognition has emerged as another key concept. Although cognition relates to speech perception, the exact nature of the relationship remains to be fully understood. This study investigates how different aspects of cognition, particularly working memory and attention, relate to speech intelligibility for various tests. Perceptual accuracy of speech perception represents just one aspect of functioning in a listening environment. Activity and participation limits imposed by hearing loss, in addition to the demands of a listening environment, are also important and may be better captured by self-report questionnaires. Understanding how speech perception relates to self-reported aspects of listening forms the second focus of the study. Forty-four listeners aged between 50 and 74 years with mild sensorineural hearing loss were tested on speech perception tests differing in complexity from low (phoneme discrimination in quiet), to medium (digit triplet perception in speech-shaped noise) to high (sentence perception in modulated noise); cognitive tests of attention, memory, and non-verbal intelligence quotient; and self-report questionnaires of general health-related and hearing-specific quality of life. Hearing sensitivity and cognition related to intelligibility differently depending on the speech test: neither was important for phoneme discrimination, hearing sensitivity alone was important for digit triplet perception, and hearing and cognition together played a role in sentence perception. Self-reported aspects of auditory functioning were correlated with speech intelligibility to different degrees, with digit triplets in noise showing the richest pattern. The results suggest that intelligibility tests can vary in their auditory and cognitive demands and their sensitivity to the challenges that auditory environments pose on functioning.