A Study of LY2541546 in Healthy Postmenopausal Women

Inclusion Criteria: * Healthy postmenopausal females, as determined by medical history and physical examination * Body mass index (BMI) at screening between 19.0 and 32.0 kilograms per square meter (kg/m\^2), inclusive * Acceptable Clinical laboratory test results, blood pressure and heart rate * Have given written informed consent * Additional Inclusion Criterion for Participants in Open Label Groups: Are currently taking or recently discontinued (not more than 3 months prior to study randomization) alendronate and have taken alendronate for at least 12 of the last 18 months Exclusion Criteria: * Within 30 days of the initial dose of study drug, have received treatment with a drug that has not received regulatory approval for any indication * Known allergies to LY2541546, its constituents, or related compounds * Persons who have previously participated in this study * History or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, or neurological disorders * History of or high risk for adverse outcome from bleeding, for example, transient ischemic attacks, cerebrovascular attacks, and ulcer disease * Paget's disease, parathyroid disease, or thyroid disease * Fracture of a long bone within 12 weeks of screening * Regular use of known drugs of abuse and/or positive findings on urinary drug screening * Evidence of human immunodeficiency virus (HIV), hepatitis C, hepatitis B and/or positive for anti-HIV antibodies, hepatitis C antibody, or hepatitis B surface antigen * Current use of therapies for osteoporosis or use of hormone replacement therapy (HRT) within the previous 12 months * Blood donation within the last month * Participants who have an average weekly alcohol intake that exceeds 14 units per week * Cigarette consumption of more than 10 cigarettes per day, or are unable or unwilling to refrain from nicotine during Clinical Research Unit (CRU) confinement Additional Exclusion Criterion for Participants in Double Blind Groups Only * Have received bisphosphonates during the previous 24 months. Additional Exclusion Criterion for Participants in Open Label Groups * Have received intravenous bisphosphonates within the previous 18 months