This study will compare two approaches to cognitive rehabilitation in adults with stroke with persistent, mild to moderate, cognitive impairment. Both approaches will feature a web-based computer game that trains cognitive processing speed, i.e., how quickly individuals process information that they receive through their senses. This training is termed Speed of Processing Training (SOPT). One approach will add (A) in-lab training on everyday activities with important cognitive components and (B) procedures designed to transfer improvements in cognition from the treatment setting to everyday life. This approach is termed Constraint-Induced Cognitive Therapy (CICT). The other approach will add (A) in-lab training on relaxation, healthy nutrition, and healthy sleep and (B) procedures designed to promote integration of these lifestyle changes into everyday life. This approach is termed Brain Fitness-Heath Education Lifestyle Program (BF-HELP). Both CICT and BF-HELP will involve 35 hours of training. Ten 1-hour sessions of SOPT will be scheduled in the home with training conducted independently by participants. Ten 2.5 hours of in-lab, face-to-face, therapist directed sessions will be scheduled. These sessions will feature a brief period of SOPT; the bulk of the sessions will be committed to in-lab training on the target behaviors and the procedures designed to promote transfer of therapeutic gains to daily life; The set of the latter procedures is termed the Transfer Package. To accommodate the demands of participants' other activities, training sessions will be permitted to be scheduled as tightly as every weekday over 2 weeks or as loosely as every other weekday or so over 4 weeks. Family caregivers in both groups will also receive training on how to best support participants in their therapeutic program. The study will also test if there is an advantage to placing follow-up phone calls after treatment ends. The purpose of the calls will be to support transition of any behavioral changes achieved during treatment into everyday life on a long-term basis. Participants will be randomly assigned to the interventions. Testing will happen one month before treatment, one day before treatment, one day afterwards, and 6-months afterwards. Outcomes measured will include cognitive processing speed, cognitive function on laboratory tests, and spontaneous performance of everyday activities with important cognitive components in daily life.