diff --git a/doc/api_break.dox b/doc/api_break.dox
index 0f0de7f0ed9..7bdbf6e424c 100644
--- a/doc/api_break.dox
+++ b/doc/api_break.dox
@@ -1354,6 +1354,8 @@ maintains Z or M dimensions from the input points and is more efficient.
 - exportToWkt() was renamed to asWkt()
 - exportToGeoJSON() was renamed to asJson()
 - closestSegmentWithContext() now returns an extra value, indicating whether the point is to the left of the geometry
+- equals() now performs a fast, strict equality check, where geometries are considered equal only if they have the
+exact same type, vertices and order. The slower topological test can be performed by calling isGeosEqual instead.
 
 
 QgsGeometryAnalyzer        {#qgis_api_break_3_0_QgsGeometryAnalyzer}
diff --git a/python/core/geometry/qgsgeometry.sip b/python/core/geometry/qgsgeometry.sip
index 8052c142c3d..4a29a91f1d6 100644
--- a/python/core/geometry/qgsgeometry.sip
+++ b/python/core/geometry/qgsgeometry.sip
@@ -249,11 +249,44 @@ return true for isEmpty().
 Returns true if WKB of the geometry is of WKBMulti* type
 %End
 
-    bool isGeosEqual( const QgsGeometry & ) const;
+    bool equals( const QgsGeometry &geometry ) const;
 %Docstring
-Compares the geometry with another geometry using GEOS
+Test if this geometry is exactly equal to another ``geometry``.
+
+This is a strict equality check, where the underlying geometries must
+have exactly the same type, component vertices and vertex order.
+
+Calling this method is dramatically faster than the topological
+equality test performed by isGeosEqual().
+
+.. note::
+
+   Comparing two null geometries will return false.
 
 .. versionadded:: 1.5
+
+.. seealso:: :py:func:`isGeosEqual()`
+%End
+
+    bool isGeosEqual( const QgsGeometry & ) const;
+%Docstring
+Compares the geometry with another geometry using GEOS.
+
+This method performs a slow, topological check, where geometries
+are considered equal if all of the their component edges overlap. E.g.
+lines with the same vertex locations but opposite direction will be
+considered equal by this method.
+
+Consider using the much faster, stricter equality test performed
+by equals() instead.
+
+.. note::
+
+   Comparing two null geometries will return false.
+
+.. versionadded:: 1.5
+
+.. seealso:: :py:func:`equals()`
 %End
 
     bool isGeosValid() const;
@@ -749,13 +782,6 @@ Tests for if geometry is contained in another (uses GEOS)
 %Docstring
 Tests for if geometry is disjoint of another (uses GEOS)
 
-.. versionadded:: 1.5
-%End
-
-    bool equals( const QgsGeometry &geometry ) const;
-%Docstring
-Test for if geometry equals another (uses GEOS)
-
 .. versionadded:: 1.5
 %End
 
diff --git a/src/core/geometry/qgsgeometry.cpp b/src/core/geometry/qgsgeometry.cpp
index 14010b78e11..a995194ccf5 100644
--- a/src/core/geometry/qgsgeometry.cpp
+++ b/src/core/geometry/qgsgeometry.cpp
@@ -1147,9 +1147,12 @@ bool QgsGeometry::equals( const QgsGeometry &geometry ) const
     return false;
   }
 
-  QgsGeos geos( d->geometry.get() );
-  mLastError.clear();
-  return geos.isEqual( geometry.d->geometry.get(), &mLastError );
+  // fast check - are they shared copies of the same underlying geometry?
+  if ( d == geometry.d )
+    return true;
+
+  // slower check - actually test the geometries
+  return *d->geometry.get() == *geometry.d->geometry.get();
 }
 
 bool QgsGeometry::touches( const QgsGeometry &geometry ) const
diff --git a/src/core/geometry/qgsgeometry.h b/src/core/geometry/qgsgeometry.h
index 9d5b674e4f3..f66c16a3b47 100644
--- a/src/core/geometry/qgsgeometry.h
+++ b/src/core/geometry/qgsgeometry.h
@@ -307,8 +307,36 @@ class CORE_EXPORT QgsGeometry
     bool isMultipart() const;
 
     /**
-     * Compares the geometry with another geometry using GEOS
+     * Test if this geometry is exactly equal to another \a geometry.
+     *
+     * This is a strict equality check, where the underlying geometries must
+     * have exactly the same type, component vertices and vertex order.
+     *
+     * Calling this method is dramatically faster than the topological
+     * equality test performed by isGeosEqual().
+     *
+     * \note Comparing two null geometries will return false.
+     *
      * \since QGIS 1.5
+     * \see isGeosEqual()
+     */
+    bool equals( const QgsGeometry &geometry ) const;
+
+    /**
+     * Compares the geometry with another geometry using GEOS.
+     *
+     * This method performs a slow, topological check, where geometries
+     * are considered equal if all of the their component edges overlap. E.g.
+     * lines with the same vertex locations but opposite direction will be
+     * considered equal by this method.
+     *
+     * Consider using the much faster, stricter equality test performed
+     * by equals() instead.
+     *
+     * \note Comparing two null geometries will return false.
+     *
+     * \since QGIS 1.5
+     * \see equals()
      */
     bool isGeosEqual( const QgsGeometry & ) const;
 
@@ -790,12 +818,6 @@ class CORE_EXPORT QgsGeometry
      */
     bool disjoint( const QgsGeometry &geometry ) const;
 
-    /**
-     * Test for if geometry equals another (uses GEOS)
-     *  \since QGIS 1.5
-     */
-    bool equals( const QgsGeometry &geometry ) const;
-
     /**
      * Test for if geometry touch another (uses GEOS)
      *  \since QGIS 1.5
diff --git a/src/core/qgsvectorlayer.cpp b/src/core/qgsvectorlayer.cpp
old mode 100644
new mode 100755
index b6a3f55fb59..34db27ec086
--- a/src/core/qgsvectorlayer.cpp
+++ b/src/core/qgsvectorlayer.cpp
@@ -985,7 +985,7 @@ bool QgsVectorLayer::updateFeature( const QgsFeature &updatedFeature, bool skipD
     bool hasChanged = false;
     bool hasError = false;
 
-    if ( ( updatedFeature.hasGeometry() || currentFeature.hasGeometry() ) && !updatedFeature.geometry().isGeosEqual( currentFeature.geometry() ) )
+    if ( ( updatedFeature.hasGeometry() || currentFeature.hasGeometry() ) && !updatedFeature.geometry().equals( currentFeature.geometry() ) )
     {
       if ( changeGeometry( updatedFeature.id(), updatedFeature.geometry(), true ) )
       {
diff --git a/tests/src/core/testqgsgeometry.cpp b/tests/src/core/testqgsgeometry.cpp
index fe8cdb1ef80..32b61ff0486 100644
--- a/tests/src/core/testqgsgeometry.cpp
+++ b/tests/src/core/testqgsgeometry.cpp
@@ -80,8 +80,10 @@ class TestQgsGeometry : public QObject
     void asVariant(); //test conversion to and from a QVariant
     void isEmpty();
     void operatorBool();
+    void equality();
     void vertexIterator();
 
+
     // geometry types
     void point(); //test QgsPointV2
     void lineString(); //test QgsLineString
@@ -431,6 +433,43 @@ void TestQgsGeometry::operatorBool()
   QVERIFY( !geom );
 }
 
+void TestQgsGeometry::equality()
+{
+  // null geometries
+  QVERIFY( !QgsGeometry().equals( QgsGeometry() ) );
+
+  // compare to null
+  QgsGeometry g1( qgis::make_unique< QgsPoint >( 1.0, 2.0 ) );
+  QVERIFY( !g1.equals( QgsGeometry() ) );
+  QVERIFY( !QgsGeometry().equals( g1 ) );
+
+  // compare implicitly shared copies
+  QgsGeometry g2( g1 );
+  QVERIFY( g2.equals( g1 ) );
+  QVERIFY( g1.equals( g2 ) );
+  QVERIFY( g1.equals( g1 ) );
+
+  // equal geometry, but different internal data
+  g2 = QgsGeometry::fromWkt( "Point( 1.0 2.0 )" );
+  QVERIFY( g2.equals( g1 ) );
+  QVERIFY( g1.equals( g2 ) );
+
+  // different dimensionality
+  g2 = QgsGeometry::fromWkt( "PointM( 1.0 2.0 3.0)" );
+  QVERIFY( !g2.equals( g1 ) );
+  QVERIFY( !g1.equals( g2 ) );
+
+  // different type
+  g2 = QgsGeometry::fromWkt( "LineString( 1.0 2.0, 3.0 4.0 )" );
+  QVERIFY( !g2.equals( g1 ) );
+  QVERIFY( !g1.equals( g2 ) );
+
+  // different direction
+  g1 = QgsGeometry::fromWkt( "LineString( 3.0 4.0, 1.0 2.0 )" );
+  QVERIFY( !g2.equals( g1 ) );
+  QVERIFY( !g1.equals( g2 ) );
+}
+
 void TestQgsGeometry::vertexIterator()
 {
   QgsGeometry geom;