diff --git a/checker/tests/nullness/Issue6635.java b/checker/tests/nullness/Issue6635.java
new file mode 100644
index 00000000000..f4bda6af07c
--- /dev/null
+++ b/checker/tests/nullness/Issue6635.java
@@ -0,0 +1,27 @@
+import org.checkerframework.checker.nullness.qual.NonNull;
+import org.checkerframework.checker.nullness.qual.Nullable;
+
+public class Issue6635 {
+  @FunctionalInterface
+  public interface ThrowingRunnable<X extends Throwable> {
+    void run() throws X;
+  }
+
+  @FunctionalInterface
+  public interface ThrowingConsumer<T, X extends Throwable> {
+    void accept(T t) throws X;
+  }
+
+  public static ThrowingRunnable<Exception> closing(@Nullable AutoCloseable resource) {
+    return disposing(resource, AutoCloseable::close);
+  }
+
+  public static <T extends @NonNull Object, X extends Throwable> ThrowingRunnable<X> disposing(
+      @Nullable T resource, ThrowingConsumer<? super T, X> disposer) {
+    return () -> {
+      if (resource != null) {
+        disposer.accept(resource);
+      }
+    };
+  }
+}
diff --git a/framework/src/main/java/org/checkerframework/framework/util/typeinference8/types/InferenceFactory.java b/framework/src/main/java/org/checkerframework/framework/util/typeinference8/types/InferenceFactory.java
index f21b0c89511..62877ee413c 100644
--- a/framework/src/main/java/org/checkerframework/framework/util/typeinference8/types/InferenceFactory.java
+++ b/framework/src/main/java/org/checkerframework/framework/util/typeinference8/types/InferenceFactory.java
@@ -977,7 +977,12 @@ public ConstraintSet getCheckedExceptionConstraints(
       if (ei.isProper()) {
         properTypes.add((ProperType) ei);
       } else {
-        es.add((UseOfVariable) ei);
+        UseOfVariable varEi = (UseOfVariable) ei;
+        if (varEi.getVariable().getInstantiation() != null) {
+          properTypes.add(varEi.getVariable().getInstantiation());
+        } else {
+          es.add((UseOfVariable) ei);
+        }
       }
     }
     if (es.isEmpty()) {