Small- and medium-sized enterprises (SMEs) account for two-thirds of employment in the euro area which makes them a priority for the transmission of monetary policy to the real economy. SMEs in Europe experienced a credit crunch following the sovereign debt crisis. Over the period 2014–2019, the European Central Bank (ECB) engaged in unconventional monetary policy (UMP) to restore funding conditions in the euro area, to support stronger economic growth and higher inflation. We use the ECB/EC Survey on the Access to Finance of Enterprises to examine the relationship between monetary policy and SME access to finance in countries that were most affected by the crisis as follows: Greece, Ireland, Italy, Portugal and Spain. We show that the implementation of UMP increases the probability that firms with higher debt-to-assets ratio remain credit constrained in stressed countries, although this effect becomes insignificant in non-stressed countries. Our findings suggest that monetary policy is transmitted unevenly to leveraged SMEs across jurisdictions. Additionally, we find little evidence that risky firms are credit constrained during periods of UMP, when risk is measured from the firms’ own viewpoint. However, our heterogenous analysis shows that smaller and younger firms—which are also considered to be risky—remain credit constrained over this period. Policy should ensure that UMP trickles down to SMEs regardless of their size, age or location. Tweetable line: Leveraged SMEs in stressed countries are more likely to remain credit constrained even when monetary policy is expansionary. Policy must do more to support small and young firms’ access to credit to facilitate higher investment and growth.