The main purpose of this study is to look at the effect of ketoconazole and fluconazole on how much baricitinib gets into the blood stream. The study will also look at the tolerability of baricitinib and ketoconazole when given together and the tolerability of baricitinib and fluconazole when given together.

Participants will be recruited into 1 of 2 treatment groups (Group A or Group B). Each treatment group will participate in 2 study periods. Participants will take baricitinib alone in 1 period and baricitinib with either ketoconazole or fluconazole in the other period. This study will last approximately 7 weeks.

Inclusion Criteria:

• Overtly healthy as determined by medical history and physical examination
• Female participants not of childbearing potential due to surgical sterilization (at least 3 months after surgical hysterectomy, bilateral oophorectomy with or without hysterectomy, or bilateral tubal occlusion/ligation) confirmed by medical history or menopause
• Have a body mass index of 18 to 29 kilograms per square meter (kg/m^2), inclusive, at screening

Exclusion Criteria:

• Participants who have previously completed or withdrawn from this study or any other study investigating baricitinib, and have previously received the study drug
• Have known allergies to baricitinib, ketoconazole, fluconazole, related compounds, or any components of the baricitinib, ketoconazole, or fluconazole formulations, or history of significant atopy
• Have a history of or current cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data
• Have a current or recent history [less than 30 days prior to screening and/or less than 45 days prior to day of admission to Clinical Research Unit (CRU)] of a clinically significant bacterial, fungal, parasitic, viral (not including rhinopharyngitis), or mycobacterial infection
• Have alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase, total bilirubin, or gamma glutamyl transferase (GGT) values above the upper limit of the reference range for the local laboratory at screening or day of admission to CRU
• Have an absolute neutrophil count (ANC) less than 2 times 10^9 per liter (L) [2000 cells per microliter (μL)] at screening or day of admission to CRU. For abnormal values, a single repeat will be allowed
• Intend to use over-the-counter or prescription medication and/or herbal supplements within 14 days prior to dosing and during the study (with the exception of occasional paracetamol, which will be permitted at the discretion of the investigator), or intended use of vitamin supplements from Day 1 until discharge from the CRU
• Have used or intend to use any drugs or substances that are known to be substrates, inhibitors, or inducers of cytochrome P450 (CYP) 3A4, CYP2C9, or CYP2C19 within 30 days prior to dosing and throughout the study

All enrolled participants.

Baseline through study completion (up to Day 23).