I would consider a CD ladder. Put $3k into each if 5 CDs (or $5k into 3 CDs). Each CD will have a different maturity, so like 3mo, 6 mo, 9mo, 12mo, 15mo. (Or whatever works for you). When a CD matures, roll it over so that you'll still have a CD expiring every 3-6months. In an emergency, you can withdraw from a CD- you just risk losing some interest. If you ladder, you can choose to close as many CDs as you need, but this protects the interest in the accounts you don't need to withdraw from.
This is what we do with our emergency fund. We're getting the best interest we can without risk to the capital, and having to close 1-2 CDs early in an emergency is an acceptable risk for us.