diff --git a/python/src/com/jetbrains/python/codeInsight/completion/PythonCompletionWeigher.java b/python/src/com/jetbrains/python/codeInsight/completion/PythonCompletionWeigher.java
index c4d0010cdefc..14157a977fdd 100644
--- a/python/src/com/jetbrains/python/codeInsight/completion/PythonCompletionWeigher.java
+++ b/python/src/com/jetbrains/python/codeInsight/completion/PythonCompletionWeigher.java
@@ -33,6 +33,7 @@ public class PythonCompletionWeigher extends CompletionWeigher {
 
   public static final int WEIGHT_DELTA = 5;
 
+  @NonNls private static final String SINGLE_UNDER = "_";
   @NonNls private static final String DOUBLE_UNDER = "__";
 
   @Override
@@ -48,8 +49,11 @@ public class PythonCompletionWeigher extends CompletionWeigher {
       return element.getLookupString().length();
     }
     if (name.startsWith(DOUBLE_UNDER)) {
-      if (name.endsWith(DOUBLE_UNDER)) return -2 * WEIGHT_DELTA; // __foo__ is lowest
-      else return -WEIGHT_DELTA; // __foo is lower than normal
+      if (name.endsWith(DOUBLE_UNDER)) return -4 * WEIGHT_DELTA; // __foo__ is lowest
+      else return -2 * WEIGHT_DELTA; // __foo is lower than normal
+    }
+    if (name.startsWith(SINGLE_UNDER)) {
+      return -1 * WEIGHT_DELTA;
     }
     return 0; // default
   }
diff --git a/python/testData/completion/underscoredItemsOrderFromModuleImport/a.py b/python/testData/completion/underscoredItemsOrderFromModuleImport/a.py
new file mode 100644
index 000000000000..8cb0330a11d8
--- /dev/null
+++ b/python/testData/completion/underscoredItemsOrderFromModuleImport/a.py
@@ -0,0 +1 @@
+from m1 import <caret>
diff --git a/python/testData/completion/underscoredItemsOrderFromModuleImport/m1.py b/python/testData/completion/underscoredItemsOrderFromModuleImport/m1.py
new file mode 100644
index 000000000000..fd3713f09983
--- /dev/null
+++ b/python/testData/completion/underscoredItemsOrderFromModuleImport/m1.py
@@ -0,0 +1,23 @@
+class A:
+    pass
+
+class _A:
+    pass
+
+class __A:
+    pass
+
+class B:
+    pass
+
+def f():
+    pass
+
+def _f():
+    pass
+
+def __f():
+    pass
+
+def _g():
+    pass
diff --git a/python/testData/completion/underscoredItemsOrderModuleImport/a.py b/python/testData/completion/underscoredItemsOrderModuleImport/a.py
new file mode 100644
index 000000000000..7d8aef0196fe
--- /dev/null
+++ b/python/testData/completion/underscoredItemsOrderModuleImport/a.py
@@ -0,0 +1,2 @@
+import m1
+m1.<caret>
\ No newline at end of file
diff --git a/python/testData/completion/underscoredItemsOrderModuleImport/m1.py b/python/testData/completion/underscoredItemsOrderModuleImport/m1.py
new file mode 100644
index 000000000000..fd3713f09983
--- /dev/null
+++ b/python/testData/completion/underscoredItemsOrderModuleImport/m1.py
@@ -0,0 +1,23 @@
+class A:
+    pass
+
+class _A:
+    pass
+
+class __A:
+    pass
+
+class B:
+    pass
+
+def f():
+    pass
+
+def _f():
+    pass
+
+def __f():
+    pass
+
+def _g():
+    pass
diff --git a/python/testSrc/com/jetbrains/python/PythonCompletionTest.java b/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
index 8f8890f7be6b..e24c215c5c91 100644
--- a/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
+++ b/python/testSrc/com/jetbrains/python/PythonCompletionTest.java
@@ -42,6 +42,15 @@ public class PythonCompletionTest extends PyTestCase {
     myFixture.checkResultByFile(getTestName(true) + "/a.after.py");
   }
 
+  private void doMultiFileTestAssertSameOrderedElements(String... variants) {
+    myFixture.copyDirectoryToProject(getTestName(true), "");
+    myFixture.configureByFile("a.py");
+    myFixture.completeBasic();
+    final List<String> suggested = myFixture.getLookupElementStrings();
+    assertNotNull(suggested);
+    assertOrderedEquals(suggested, variants);
+  }
+
   @Nullable
   private List<String> doTestByText(@NotNull String text) {
     myFixture.configureByText(PythonFileType.INSTANCE, text);
@@ -1262,22 +1271,23 @@ public class PythonCompletionTest extends PyTestCase {
   // PY-28461
   public void testImplicitImportsInsidePackage() {
     runWithLanguageLevel(LanguageLevel.PYTHON37,
-                         () -> doMultiFileAssertSameElements("m1", "pkg2", "pkg3", "bar", "foo", "foo2"));
+                         () -> doMultiFileTestAssertSameOrderedElements("bar", "foo", "foo2", "m1", "pkg2", "pkg3"));
   }
 
   // PY-28461
   public void testImplicitImportsInsidePackagePy2() {
     runWithLanguageLevel(LanguageLevel.PYTHON27,
-                         () -> doMultiFileAssertSameElements("m1", "pkg2", "pkg3", "bar", "foo", "foo2"));
+                         () -> doMultiFileTestAssertSameOrderedElements("bar", "foo", "foo2", "m1", "pkg2", "pkg3"));
   }
 
-  private void doMultiFileAssertSameElements(String... variants) {
-    myFixture.copyDirectoryToProject(getTestName(true), "");
-    myFixture.configureByFile("a.py");
-    myFixture.completeBasic();
-    final List<String> suggested = myFixture.getLookupElementStrings();
-    assertNotNull(suggested);
-    assertSameElements(suggested, variants);
+  // PY-3674
+  public void testUnderscoredItemsOrderModuleImport() {
+    doMultiFileTestAssertSameOrderedElements("A", "B", "f", "_A", "_f", "_g", "__A", "__f");
+  }
+
+  // PY-3674
+  public void testUnderscoredItemsOrderFromModuleImport() {
+    doMultiFileTestAssertSameOrderedElements("A", "B", "f", "_A", "_f", "_g", "__A", "__f");
   }
 
   // PY-17810