diff --git a/jetty-server/src/test/java/org/eclipse/jetty/server/ssl/SniSslConnectionFactoryTest.java b/jetty-server/src/test/java/org/eclipse/jetty/server/ssl/SniSslConnectionFactoryTest.java
index 9b78f593977..91954a40065 100644
--- a/jetty-server/src/test/java/org/eclipse/jetty/server/ssl/SniSslConnectionFactoryTest.java
+++ b/jetty-server/src/test/java/org/eclipse/jetty/server/ssl/SniSslConnectionFactoryTest.java
@@ -40,6 +40,7 @@ import javax.net.ssl.SSLSocketFactory;
 import javax.servlet.http.HttpServletRequest;
 import javax.servlet.http.HttpServletResponse;
 
+import org.eclipse.jetty.http.HttpStatus;
 import org.eclipse.jetty.http.HttpTester;
 import org.eclipse.jetty.http.HttpVersion;
 import org.eclipse.jetty.io.Connection;
@@ -489,6 +490,21 @@ public class SniSslConnectionFactoryTest
         assertEquals(0, history.size());
     }
 
+    @Test
+    public void testSNIWithDifferentKeyTypes() throws Exception
+    {
+        // This KeyStore contains 2 certificates, one with keyAlg=EC, one with keyAlg=RSA.
+        start(ssl -> ssl.setKeyStorePath("src/test/resources/keystore_sni_key_types.p12"));
+
+        // Make a request with SNI = rsa.domain.com, the RSA certificate should be chosen.
+        HttpTester.Response response1 = HttpTester.parseResponse(getResponse("rsa.domain.com", "rsa.domain.com"));
+        assertEquals(HttpStatus.OK_200, response1.getStatus());
+
+        // Make a request with SNI = ec.domain.com, the EC certificate should be chosen.
+        HttpTester.Response response2 = HttpTester.parseResponse(getResponse("ec.domain.com", "ec.domain.com"));
+        assertEquals(HttpStatus.OK_200, response2.getStatus());
+    }
+
     private String getResponse(String host, String cn) throws Exception
     {
         String response = getResponse(host, host, cn);
diff --git a/jetty-server/src/test/resources/keystore_sni_key_types.p12 b/jetty-server/src/test/resources/keystore_sni_key_types.p12
new file mode 100644
index 00000000000..b000fbeff57
Binary files /dev/null and b/jetty-server/src/test/resources/keystore_sni_key_types.p12 differ
diff --git a/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SniX509ExtendedKeyManager.java b/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SniX509ExtendedKeyManager.java
index db05a0f6afc..2c55cdec1f8 100644
--- a/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SniX509ExtendedKeyManager.java
+++ b/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SniX509ExtendedKeyManager.java
@@ -250,7 +250,7 @@ public class SniX509ExtendedKeyManager extends X509ExtendedKeyManager
          * <p>Selects a certificate based on SNI information.</p>
          * <p>This method may be invoked multiple times during the TLS handshake, with different parameters.
          * For example, the {@code keyType} could be different, and subsequently the collection of certificates
-         * (because they need to match the {@code keyType}.</p>
+         * (because they need to match the {@code keyType}).</p>
          *
          * @param keyType the key algorithm type name
          * @param issuers the list of acceptable CA issuer subject names or null if it does not matter which issuers are used
diff --git a/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SslContextFactory.java b/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SslContextFactory.java
index 1104dbd19df..a445cad4790 100644
--- a/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SslContextFactory.java
+++ b/jetty-util/src/main/java/org/eclipse/jetty/util/ssl/SslContextFactory.java
@@ -2155,12 +2155,17 @@ public abstract class SslContextFactory extends AbstractLifeCycle implements Dum
         }
 
         /**
-         * Does the default {@link #sniSelect(String, Principal[], SSLSession, String, Collection)} implementation
-         * require an SNI match?  Note that if a non SNI handshake is accepted, requests may still be rejected
-         * at the HTTP level for incorrect SNI (see SecureRequestCustomizer).
+         * <p>Returns whether an SNI match is required when choosing the alias that
+         * identifies the certificate to send to the client.</p>
+         * <p>The exact logic to choose an alias given the SNI is configurable via
+         * {@link #setSNISelector(SniX509ExtendedKeyManager.SniSelector)}.</p>
+         * <p>The default implementation is {@link #sniSelect(String, Principal[], SSLSession, String, Collection)}
+         * and if SNI is not required it will delegate the TLS implementation to
+         * choose an alias (typically the first alias in the KeyStore).</p>
+         * <p>Note that if a non SNI handshake is accepted, requests may still be rejected
+         * at the HTTP level for incorrect SNI (see SecureRequestCustomizer).</p>
          *
-         * @return true if no SNI match is handled as no certificate match, false if no SNI match is handled by
-         * delegation to the non SNI matching methods.
+         * @return whether an SNI match is required when choosing the alias that identifies the certificate
          */
         @ManagedAttribute("Whether the TLS handshake is rejected if there is no SNI host match")
         public boolean isSniRequired()
@@ -2169,14 +2174,12 @@ public abstract class SslContextFactory extends AbstractLifeCycle implements Dum
         }
 
         /**
-         * Set if the default {@link #sniSelect(String, Principal[], SSLSession, String, Collection)} implementation
-         * require an SNI match? Note that if a non SNI handshake is accepted, requests may still be rejected
-         * at the HTTP level for incorrect SNI (see SecureRequestCustomizer).
-         * This setting may have no effect if {@link #sniSelect(String, Principal[], SSLSession, String, Collection)} is
-         * overridden or a non null function is passed to {@link #setSNISelector(SniX509ExtendedKeyManager.SniSelector)}.
+         * <p>Sets whether an SNI match is required when choosing the alias that
+         * identifies the certificate to send to the client.</p>
+         * <p>This setting may have no effect if {@link #sniSelect(String, Principal[], SSLSession, String, Collection)} is
+         * overridden or a custom function is passed to {@link #setSNISelector(SniX509ExtendedKeyManager.SniSelector)}.</p>
          *
-         * @param sniRequired true if no SNI match is handled as no certificate match, false if no SNI match is handled by
-         * delegation to the non SNI matching methods.
+         * @param sniRequired whether an SNI match is required when choosing the alias that identifies the certificate
          */
         public void setSniRequired(boolean sniRequired)
         {
@@ -2244,9 +2247,15 @@ public abstract class SslContextFactory extends AbstractLifeCycle implements Dum
                     .filter(x509 -> x509.matches(sniHost))
                     .collect(Collectors.toList());
 
-                // No match, let the JDK decide unless unmatched SNIs are rejected.
                 if (matching.isEmpty())
-                    return isSniRequired() ? null : SniX509ExtendedKeyManager.SniSelector.DELEGATE;
+                {
+                    // There is no match for this SNI among the certificates valid for
+                    // this keyType; check if there is any certificate that matches this
+                    // SNI, as we will likely be called again with a different keyType.
+                    boolean anyMatching = aliasCerts().values().stream()
+                        .anyMatch(x509 -> x509.matches(sniHost));
+                    return isSniRequired() || anyMatching ? null : SniX509ExtendedKeyManager.SniSelector.DELEGATE;
+                }
 
                 String alias = matching.get(0).getAlias();
                 if (matching.size() == 1)