diff --git a/python/src/com/jetbrains/python/inspections/PyUnresolvedReferencesInspection.java b/python/src/com/jetbrains/python/inspections/PyUnresolvedReferencesInspection.java
index 4899a2cf2ed4..eca77ef60be0 100644
--- a/python/src/com/jetbrains/python/inspections/PyUnresolvedReferencesInspection.java
+++ b/python/src/com/jetbrains/python/inspections/PyUnresolvedReferencesInspection.java
@@ -23,6 +23,7 @@ import com.jetbrains.python.psi.patterns.Matcher;
 import com.jetbrains.python.psi.patterns.ParentMatcher;
 import com.jetbrains.python.psi.patterns.SyntaxMatchers;
 import com.jetbrains.python.psi.resolve.ImportedResolveResult;
+import com.jetbrains.python.psi.resolve.ResolveImportUtil;
 import com.jetbrains.python.psi.types.*;
 import com.jetbrains.python.validation.PythonReferenceImporter;
 import org.jetbrains.annotations.Nls;
@@ -349,6 +350,17 @@ public class PyUnresolvedReferencesInspection extends PyInspection {
           if (PsiTreeUtil.getParentOfType(importStatement, PyTryExceptStatement.class) != null) {
             continue;            
           }
+          if (unusedImport instanceof PyImportElement) {
+            if (ResolveImportUtil.resolveImportElement((PyImportElement)unusedImport) == null) {
+              continue;
+            }
+          }
+          else {
+            assert importStatement instanceof PyFromImportStatement;
+            if (ResolveImportUtil.resolveFromImportStatementSource((PyFromImportStatement)importStatement) == null) {
+              continue;
+            }
+          }
           if (unusedImport instanceof PyStarImportElement || areAllImportsUnused(importStatement, unusedImports)) {
             unusedStatements.add(importStatement);
             result.add(importStatement);
diff --git a/python/testData/optimizeImports/oneOfMultiple.py b/python/testData/optimizeImports/oneOfMultiple.py
index c54e9fd4ed16..0bd810843447 100644
--- a/python/testData/optimizeImports/oneOfMultiple.py
+++ b/python/testData/optimizeImports/oneOfMultiple.py
@@ -1,2 +1,2 @@
-import sys, os
+import sys, re
 print sys.argv
diff --git a/python/testData/optimizeImports/unresolved.after.py b/python/testData/optimizeImports/unresolved.after.py
new file mode 100644
index 000000000000..b014e1fe1183
--- /dev/null
+++ b/python/testData/optimizeImports/unresolved.after.py
@@ -0,0 +1 @@
+import xyzzy_shazam
diff --git a/python/testData/optimizeImports/unresolved.py b/python/testData/optimizeImports/unresolved.py
new file mode 100644
index 000000000000..b014e1fe1183
--- /dev/null
+++ b/python/testData/optimizeImports/unresolved.py
@@ -0,0 +1 @@
+import xyzzy_shazam
diff --git a/python/testSrc/com/jetbrains/python/PyOptimizeImportsTest.java b/python/testSrc/com/jetbrains/python/PyOptimizeImportsTest.java
index 8b2806c68abd..6344af447554 100644
--- a/python/testSrc/com/jetbrains/python/PyOptimizeImportsTest.java
+++ b/python/testSrc/com/jetbrains/python/PyOptimizeImportsTest.java
@@ -8,31 +8,35 @@ import com.jetbrains.python.fixtures.PyLightFixtureTestCase;
  * @author yole
  */
 public class PyOptimizeImportsTest extends PyLightFixtureTestCase {
-  public void testSimple() throws Exception {
+  public void testSimple() {
     doTest();
   }
 
-  public void testOneOfMultiple() throws Exception {
+  public void testOneOfMultiple() {
     doTest();
   }
 
-  public void testImportStar() throws Exception {
+  public void testImportStar() {
     doTest();
   }
 
-  public void testImportStarOneOfMultiple() throws Exception {
+  public void testImportStarOneOfMultiple() {
     doTest();
   }
 
-  public void testTryExcept() throws Exception {
+  public void testTryExcept() {
     doTest();
   }
 
-  public void testFromFuture() throws Exception {
+  public void testFromFuture() {
     doTest();
   }
 
-  private void doTest() throws Exception {
+  public void testUnresolved() {  // PY-2201
+    doTest();
+  }
+
+  private void doTest() {
     myFixture.configureByFile("optimizeImports/" + getTestName(true) + ".py");
     OptimizeImportsAction.actionPerformedImpl(DataManager.getInstance().getDataContext(myFixture.getEditor().getContentComponent()));
     myFixture.checkResultByFile("optimizeImports/" + getTestName(true) + ".after.py");