This paper examines the pass-through of European Central Bank (ECB) monetary policy to deposit rates in Bosnia and Herzegovina (B&H). We use aggregate and bank-level data to study interest rate pass-through by bank size and ownership for the period 2012-2023. In extensions, we also study pass-through by counterparty and maturity of deposit contracts. Our results suggest that average pass-through is slow and incomplete. We document that pass-through is faster and more complete for banks which are small and foreign-owned, as compared to banks which are large (and foreign-owned), or banks which are small and domestic. This finding suggests that pass-through depends both on domestic market power of banks as well as their access to foreign money markets.