Subjects' ratings of the apparent randomness of ten binary sequences were compared to the time required to memorize those same sequences. Memorization time proved a better predictor of the subjective randomness ratings than measures of the "objective" randomness of the sequences. This result is interpreted as supporting the hypothesis that randomness judgments are mediated by subjective assessments of encoding difficult. Such assessments are seen as compatible with the information theorists' interpretation of randomness as complexity.