Inclusion Criteria:

• Have type 2 diabetes.
• Have been taking insulin glargine at a dose of ≥20 units/day for at least 3 months before entering the study.

Have been taking insulin glargine alone or in combination with one of the following for at least 3 months before entering the study:

1. metformin (stable dose for 6 weeks)
2. pioglitazone (stable dose for 6 weeks)

3. a combination of metformin and pioglitazone (stable dose for 6 weeks)

   • Have HbA1C between 7.1% and 10.5%, inclusive.
   • Have a body mass index (BMI) ≤45 kg/m2.
   • Have a history of stable body weight (not varying by >5% for at least 3 months prior to screening).

Exclusion Criteria:

• Have taken medications to lower blood sugar other than insulin glargine, pioglitazone, or metformin in the 3 months before entering the study for more than a 1-week period, or within 1 week of entering the study.
• Have had more than one episode of major (severe) hypoglycemia in the 6 months before entering the study.
• Are pregnant or intend to become pregnant during the study or are sexually active women not actively practicing birth control.
• Women who are breastfeeding.
• Have any significant diseases of the blood, heart, kidney, gastrointestinal system, or other significant diseases such as cancer.
• Have had a kidney transplant or are currently on kidney dialysis.
• Have a cancer that's never been treated, that's currently being treated, or that was diagnosed within the last 5 years.
• Have had a bad reaction to exenatide in the past or have a condition that is not recommended to be exposed to exenatide or any of exenatide's other ingredients.
• Have used a drug for weight loss in the 3 months before entering the study for more than a 1-week period, or within 1 month of entering the study.
• Are currently on a weight-loss program or have been on one within 3 months of entering the study.
• Have had a blood transfusion or severe blood loss within 3 months of entering the study.
• Are taking systemic glucocorticoids or have received systemic glucocorticoids within 8 weeks of entering the study.
• Have an irregular sleep cycle (for example, sleeping during the day and working during the night).
• Have a history of pancreatitis.
• Have received treatment with an experimental drug within 30 days of entering the study.
• If on metformin, have a condition that is not recommended to be exposed to metformin, or any condition associated with hypoperfusion, hypoxemia, dehydration, or sepsis.
• If on metformin, have had a radiologic contrast study performed within 48 hours of entering the study.
• If on pioglitazone, have a condition that is not recommended to be exposed to pioglitazone, including congestive heart failure, or are taking pioglitazone at a dose that is not approved for use with insulin.