diff --git a/include/randr.h b/include/randr.h
index bfbfd5a9..39182c54 100644
--- a/include/randr.h
+++ b/include/randr.h
@@ -88,6 +88,14 @@ Output *get_output_by_name(const char *name, const bool require_active);
  */
 Output *get_output_containing(unsigned int x, unsigned int y);
 
+/**
+ * Returns the active output which contains the midpoint of the given rect. If
+ * such an output doesn't exist, returns the output which contains most of the
+ * rectangle or NULL if there is no output which intersects with it.
+ *
+ */
+Output *get_output_from_rect(Rect rect);
+
 /**
  * Returns the active output which spans exactly the area specified by
  * rect or NULL if there is no output like this.
@@ -95,15 +103,14 @@ Output *get_output_containing(unsigned int x, unsigned int y);
  */
 Output *get_output_with_dimensions(Rect rect);
 
-/*
- * In contained_by_output, we check if any active output contains part of the container.
+/**
+ * In output_containing_rect, we check if any active output contains part of the container.
  * We do this by checking if the output rect is intersected by the Rect.
  * This is the 2-dimensional counterpart of get_output_containing.
- * Since we don't actually need the outputs intersected by the given Rect (There could
- * be many), we just return true or false for convenience.
+ * Returns the output with the maximum intersecting area.
  *
  */
-bool contained_by_output(Rect rect);
+Output *output_containing_rect(Rect rect);
 
 /**
  * Gets the output which is the next one in the given direction.
diff --git a/src/floating.c b/src/floating.c
index 2130d673..fc68df8e 100644
--- a/src/floating.c
+++ b/src/floating.c
@@ -284,10 +284,7 @@ void floating_enable(Con *con, bool automatic) {
 
     /* Sanity check: Are the coordinates on the appropriate output? If not, we
      * need to change them */
-    Output *current_output = get_output_containing(nc->rect.x +
-                                                       (nc->rect.width / 2),
-                                                   nc->rect.y + (nc->rect.height / 2));
-
+    Output *current_output = get_output_from_rect(nc->rect);
     Con *correct_output = con_get_output(ws);
     if (!current_output || current_output->con != correct_output) {
         DLOG("This floating window is on the wrong output, fixing coordinates (currently (%d, %d))\n",
@@ -295,11 +292,13 @@ void floating_enable(Con *con, bool automatic) {
 
         /* If moving from one output to another, keep the relative position
          * consistent (e.g. a centered dialog will remain centered). */
-        if (current_output)
+        if (current_output) {
             floating_fix_coordinates(nc, &current_output->con->rect, &correct_output->rect);
-        else {
-            nc->rect.x = correct_output->rect.x;
-            nc->rect.y = correct_output->rect.y;
+            /* Make sure that the result is in the correct output. */
+            current_output = get_output_from_rect(nc->rect);
+        }
+        if (!current_output || current_output->con != correct_output) {
+            floating_center(nc, ws->rect);
         }
     }
 
@@ -320,21 +319,6 @@ void floating_enable(Con *con, bool automatic) {
     if (set_focus)
         con_activate(con);
 
-    /* Check if we need to re-assign it to a different workspace because of its
-     * coordinates and exit if that was done successfully. */
-    if (floating_maybe_reassign_ws(nc)) {
-        goto done;
-    }
-
-    /* Sanitize coordinates: Check if they are on any output */
-    if (get_output_containing(nc->rect.x, nc->rect.y) != NULL) {
-        goto done;
-    }
-
-    ELOG("No output found at destination coordinates, centering floating window on current ws\n");
-    floating_center(nc, ws->rect);
-
-done:
     floating_set_hint_atom(nc, true);
     ipc_send_window_event("floating", con);
 }
@@ -429,9 +413,7 @@ void floating_raise_con(Con *con) {
  *
  */
 bool floating_maybe_reassign_ws(Con *con) {
-    Output *output = get_output_containing(
-        con->rect.x + (con->rect.width / 2),
-        con->rect.y + (con->rect.height / 2));
+    Output *output = get_output_from_rect(con->rect);
 
     if (!output) {
         ELOG("No output found at destination coordinates?\n");
@@ -867,7 +849,7 @@ drag_result_t drag_pointer(Con *con, const xcb_button_press_event_t *event, xcb_
 bool floating_reposition(Con *con, Rect newrect) {
     /* Sanity check: Are the new coordinates on any output? If not, we
      * ignore that request. */
-    if (!contained_by_output(newrect)) {
+    if (!output_containing_rect(newrect)) {
         ELOG("No output found at destination coordinates. Not repositioning.\n");
         return false;
     }
diff --git a/src/randr.c b/src/randr.c
index 85add08f..c43c6455 100644
--- a/src/randr.c
+++ b/src/randr.c
@@ -114,6 +114,20 @@ Output *get_output_containing(unsigned int x, unsigned int y) {
     return NULL;
 }
 
+/*
+ * Returns the active output which contains the midpoint of the given rect. If
+ * such an output doesn't exist, returns the output which contains most of the
+ * rectangle or NULL if there is no output which intersects with it.
+ *
+ */
+Output *get_output_from_rect(Rect rect) {
+    unsigned int mid_x = rect.x + rect.width / 2;
+    unsigned int mid_y = rect.y + rect.height / 2;
+    Output *output = get_output_containing(mid_x, mid_y);
+
+    return output ? output : output_containing_rect(rect);
+}
+
 /*
  * Returns the active output which spans exactly the area specified by
  * rect or NULL if there is no output like this.
@@ -136,27 +150,37 @@ Output *get_output_with_dimensions(Rect rect) {
 }
 
 /*
- * In contained_by_output, we check if any active output contains part of the container.
+ * In output_containing_rect, we check if any active output contains part of the container.
  * We do this by checking if the output rect is intersected by the Rect.
  * This is the 2-dimensional counterpart of get_output_containing.
- * Since we don't actually need the outputs intersected by the given Rect (There could
- * be many), we just return true or false for convenience.
+ * Returns the output with the maximum intersecting area.
  *
  */
-bool contained_by_output(Rect rect) {
+Output *output_containing_rect(Rect rect) {
     Output *output;
     int lx = rect.x, uy = rect.y;
     int rx = rect.x + rect.width, by = rect.y + rect.height;
+    long max_area = 0;
+    Output *result = NULL;
     TAILQ_FOREACH(output, &outputs, outputs) {
         if (!output->active)
             continue;
+        int lx_o = (int)output->rect.x, uy_o = (int)output->rect.y;
+        int rx_o = (int)(output->rect.x + output->rect.width), by_o = (int)(output->rect.y + output->rect.height);
         DLOG("comparing x=%d y=%d with x=%d and y=%d width %d height %d\n",
              rect.x, rect.y, output->rect.x, output->rect.y, output->rect.width, output->rect.height);
-        if (rx >= (int)output->rect.x && lx <= (int)(output->rect.x + output->rect.width) &&
-            by >= (int)output->rect.y && uy <= (int)(output->rect.y + output->rect.height))
-            return true;
+        int left = max(lx, lx_o);
+        int right = min(rx, rx_o);
+        int bottom = min(by, by_o);
+        int top = max(uy, uy_o);
+        if (left < right && bottom > top) {
+            long area = (right - left) * (bottom - top);
+            if (area > max_area) {
+                result = output;
+            }
+        }
     }
-    return false;
+    return result;
 }
 
 /*