diff --git a/src/map/encatlas.cpp b/src/map/encatlas.cpp
index 0e40a701..20a9e4c9 100644
--- a/src/map/encatlas.cpp
+++ b/src/map/encatlas.cpp
@@ -9,6 +9,7 @@
 
 using namespace ENC;
 
+#define EPSILON   1e-6
 #define TILE_SIZE 512
 
 Range ENCAtlas::zooms(IntendedUsage usage)
@@ -204,7 +205,8 @@ int ENCAtlas::zoomFit(const QSize &size, const RectC &rect)
 				Transform t(transform(i));
 				QRectF r(t.proj2img(pr.topLeft()), t.proj2img(pr.bottomRight()));
 
-				if (size.width() < r.width() || size.height() < r.height()) {
+				if (size.width() + EPSILON < r.width()
+				  || size.height() + EPSILON < r.height()) {
 					updateTransform();
 					return _zoom;
 				}
diff --git a/src/map/encmap.cpp b/src/map/encmap.cpp
index 9eaf018d..ae318de7 100644
--- a/src/map/encmap.cpp
+++ b/src/map/encmap.cpp
@@ -12,6 +12,7 @@
 
 using namespace ENC;
 
+#define EPSILON   1e-6
 #define TILE_SIZE 512
 
 static Range zooms(const RectC &bounds)
@@ -204,7 +205,8 @@ int ENCMap::zoomFit(const QSize &size, const RectC &rect)
 		for (int i = _zooms.min() + 1; i <= _zooms.max(); i++) {
 			Transform t(transform(i));
 			QRectF r(t.proj2img(pr.topLeft()), t.proj2img(pr.bottomRight()));
-			if (size.width() < r.width() || size.height() < r.height())
+			if (size.width() + EPSILON < r.width()
+			  || size.height() + EPSILON < r.height())
 				break;
 			_zoom = i;
 		}
diff --git a/src/map/imgmap.cpp b/src/map/imgmap.cpp
index 1211debe..54a1d003 100644
--- a/src/map/imgmap.cpp
+++ b/src/map/imgmap.cpp
@@ -15,6 +15,7 @@
 
 using namespace IMG;
 
+#define EPSILON     1e-6
 #define TILE_SIZE   384
 
 static RectC limitBounds(const RectC &bounds, const Projection &proj)
@@ -112,7 +113,8 @@ int IMGMap::zoomFit(const QSize &size, const RectC &rect)
 		for (int i = zooms.min() + 1; i <= zooms.max(); i++) {
 			Transform t(transform(i));
 			QRectF r(t.proj2img(pr.topLeft()), t.proj2img(pr.bottomRight()));
-			if (size.width() < r.width() || size.height() < r.height())
+			if (size.width() + EPSILON < r.width()
+			  || size.height() + EPSILON < r.height())
 				break;
 			_zoom = i;
 		}
diff --git a/src/map/mapsforgemap.cpp b/src/map/mapsforgemap.cpp
index 0e6b9793..dc69fd1c 100644
--- a/src/map/mapsforgemap.cpp
+++ b/src/map/mapsforgemap.cpp
@@ -9,6 +9,8 @@
 
 using namespace Mapsforge;
 
+#define EPSILON     1e-6
+
 MapsforgeMap::MapsforgeMap(const QString &fileName, QObject *parent)
   : Map(fileName, parent), _data(fileName), _zoom(0),
   _projection(PCS::pcs(3857)), _tileRatio(1.0)
@@ -51,7 +53,8 @@ int MapsforgeMap::zoomFit(const QSize &size, const RectC &rect)
 		for (int i = _data.zooms().min() + 1; i <= _data.zooms().max(); i++) {
 			Transform t(transform(i));
 			QRectF r(t.proj2img(pr.topLeft()), t.proj2img(pr.bottomRight()));
-			if (size.width() < r.width() || size.height() < r.height())
+			if (size.width() + EPSILON < r.width()
+			  || size.height() + EPSILON < r.height())
 				break;
 			_zoom = i;
 		}