Prestudy treatment for patients who enter this study will be once daily insulin glargine along with mealtime insulins. Patients will continue to use their mealtime insulins throughout the study. The study will consist of 16 weeks of treatment and 4 weeks of follow-up. The 16 weeks of treatment will consist of two 8-week periods (Periods 1 and 2) during which patients will receive insulin glargine for 8 weeks and LY2605541 for 8 weeks in a random sequence. During the 4-week follow-up period, patients will return to insulin glargine or another basal insulin recommended by the investigator.