diff --git a/include/sway/tree/container.h b/include/sway/tree/container.h
index e4f74b08..4b686040 100644
--- a/include/sway/tree/container.h
+++ b/include/sway/tree/container.h
@@ -79,8 +79,7 @@ struct sway_container {
 	bool is_sticky;
 
 	// For C_ROOT, this has no meaning
-	// For C_OUTPUT, this is the output position in layout coordinates
-	// For other types, this is the position in output-local coordinates
+	// For other types, this is the position in layout coordinates
 	// Includes borders
 	double x, y;
 	double width, height;
diff --git a/include/sway/tree/view.h b/include/sway/tree/view.h
index 7a94b2c2..65a23902 100644
--- a/include/sway/tree/view.h
+++ b/include/sway/tree/view.h
@@ -29,7 +29,7 @@ struct sway_view_impl {
 	const char *(*get_string_prop)(struct sway_view *view,
 			enum sway_view_prop prop);
 	uint32_t (*get_int_prop)(struct sway_view *view, enum sway_view_prop prop);
-	void (*configure)(struct sway_view *view, double ox, double oy, int width,
+	void (*configure)(struct sway_view *view, double lx, double ly, int width,
 		int height);
 	void (*set_activated)(struct sway_view *view, bool activated);
 	void (*set_tiled)(struct sway_view *view, bool tiled);
@@ -48,7 +48,7 @@ struct sway_view {
 	struct sway_container *swayc; // NULL for unmapped views
 	struct wlr_surface *surface; // NULL for unmapped views
 
-	// Geometry of the view itself (excludes borders)
+	// Geometry of the view itself (excludes borders) in layout coordinates
 	double x, y;
 	int width, height;
 
diff --git a/sway/desktop/output.c b/sway/desktop/output.c
index fb80fd87..8600d049 100644
--- a/sway/desktop/output.c
+++ b/sway/desktop/output.c
@@ -65,6 +65,13 @@ struct root_geometry {
 	float rotation;
 };
 
+struct render_data {
+	struct root_geometry root_geo;
+	struct sway_output *output;
+	pixman_region32_t *damage;
+	float alpha;
+};
+
 static bool get_surface_box(struct root_geometry *geo,
 		struct sway_output *output, struct wlr_surface *surface, int sx, int sy,
 		struct wlr_box *surface_box) {
@@ -116,8 +123,9 @@ static void surface_for_each_surface(struct wlr_surface *surface,
 static void output_view_for_each_surface(struct sway_view *view,
 		struct root_geometry *geo, wlr_surface_iterator_func_t iterator,
 		void *user_data) {
-	geo->x = view->x;
-	geo->y = view->y;
+	struct render_data *data = user_data;
+	geo->x = view->x - data->output->wlr_output->lx;
+	geo->y = view->y - data->output->wlr_output->ly;
 	geo->width = view->surface->current->width;
 	geo->height = view->surface->current->height;
 	geo->rotation = 0; // TODO
@@ -160,13 +168,6 @@ static void scale_box(struct wlr_box *box, float scale) {
 	box->height *= scale;
 }
 
-struct render_data {
-	struct root_geometry root_geo;
-	struct sway_output *output;
-	pixman_region32_t *damage;
-	float alpha;
-};
-
 static void scissor_output(struct wlr_output *wlr_output,
 		pixman_box32_t *rect) {
 	struct wlr_renderer *renderer = wlr_backend_get_renderer(wlr_output->backend);
@@ -275,7 +276,10 @@ static void render_rect(struct wlr_output *wlr_output,
 	struct wlr_renderer *renderer =
 		wlr_backend_get_renderer(wlr_output->backend);
 
-	struct wlr_box box = *_box;
+	struct wlr_box box;
+	memcpy(&box, _box, sizeof(struct wlr_box));
+	box.x -= wlr_output->lx * wlr_output->scale;
+	box.y -= wlr_output->ly * wlr_output->scale;
 
 	pixman_region32_t damage;
 	pixman_region32_init(&damage);
@@ -450,8 +454,10 @@ static void render_titlebar(struct sway_output *output,
 		wlr_texture_get_size(marks_texture,
 			&texture_box.width, &texture_box.height);
 		texture_box.x =
-			(x + width - TITLEBAR_H_PADDING) * output_scale - texture_box.width;
-		texture_box.y = (y + TITLEBAR_V_PADDING) * output_scale;
+			(x - output->wlr_output->lx + width - TITLEBAR_H_PADDING)
+			* output_scale - texture_box.width;
+		texture_box.y = (y - output->wlr_output->ly + TITLEBAR_V_PADDING)
+			* output_scale;
 
 		float matrix[9];
 		wlr_matrix_project_box(matrix, &texture_box,
@@ -472,8 +478,10 @@ static void render_titlebar(struct sway_output *output,
 		struct wlr_box texture_box;
 		wlr_texture_get_size(title_texture,
 			&texture_box.width, &texture_box.height);
-		texture_box.x = (x + TITLEBAR_H_PADDING) * output_scale;
-		texture_box.y = (y + TITLEBAR_V_PADDING) * output_scale;
+		texture_box.x = (x - output->wlr_output->lx + TITLEBAR_H_PADDING)
+			* output_scale;
+		texture_box.y = (y - output->wlr_output->ly + TITLEBAR_V_PADDING)
+			* output_scale;
 
 		float matrix[9];
 		wlr_matrix_project_box(matrix, &texture_box,
@@ -771,28 +779,8 @@ static bool floater_intersects_output(struct sway_container *floater,
 			output->sway_output->wlr_output, &box);
 }
 
-static void container_translate(struct sway_container *con, int x, int y) {
-	con->x += x;
-	con->y += y;
-	if (con->type == C_VIEW) {
-		con->sway_view->x += x;
-		con->sway_view->y += y;
-	} else {
-		for (int i = 0; i < con->children->length; ++i) {
-			struct sway_container *child = con->children->items[i];
-			container_translate(child, x, y);
-		}
-	}
-}
-
 static void render_floating_container(struct sway_output *soutput,
 		pixman_region32_t *damage, struct sway_container *con) {
-	// We need to translate the floating container's coordinates from layout
-	// coordinates into output-local coordinates. This needs to happen for all
-	// children of the floating container too.
-	struct sway_container *output = container_parent(con, C_OUTPUT);
-	container_translate(con, -output->x, -output->y);
-
 	if (con->type == C_VIEW) {
 		struct sway_view *view = con->sway_view;
 		struct sway_seat *seat = input_manager_current_seat(input_manager);
@@ -821,8 +809,6 @@ static void render_floating_container(struct sway_output *soutput,
 	} else {
 		render_container(soutput, damage, con, false);
 	}
-	// Undo the translation
-	container_translate(con, output->x, output->y);
 }
 
 static void render_floating(struct sway_output *soutput,
@@ -1123,15 +1109,7 @@ static void output_damage_view(struct sway_output *output,
 
 void output_damage_from_view(struct sway_output *output,
 		struct sway_view *view) {
-	if (container_self_or_parent_floating(view->swayc)) {
-		view->x -= output->swayc->x;
-		view->y -= output->swayc->y;
-		output_damage_view(output, view, false);
-		view->x += output->swayc->x;
-		view->y += output->swayc->y;
-	} else {
-		output_damage_view(output, view, false);
-	}
+	output_damage_view(output, view, false);
 }
 
 static void output_damage_whole_container_iterator(struct sway_container *con,
@@ -1148,24 +1126,13 @@ static void output_damage_whole_container_iterator(struct sway_container *con,
 void output_damage_whole_container(struct sway_output *output,
 		struct sway_container *con) {
 	struct wlr_box box = {
-		.x = con->x,
-		.y = con->y,
+		.x = con->x - output->wlr_output->lx,
+		.y = con->y - output->wlr_output->ly,
 		.width = con->width,
 		.height = con->height,
 	};
-	if (container_is_floating(con)) {
-		box.x -= output->wlr_output->lx;
-		box.y -= output->wlr_output->ly;
-	}
 	scale_box(&box, output->wlr_output->scale);
 	wlr_output_damage_add_box(output->damage, &box);
-
-	if (con->type == C_VIEW) {
-		output_damage_whole_container_iterator(con, output);
-	} else {
-		container_descendants(con, C_VIEW,
-			output_damage_whole_container_iterator, output);
-	}
 }
 
 static void damage_handle_destroy(struct wl_listener *listener, void *data) {
diff --git a/sway/desktop/xdg_shell.c b/sway/desktop/xdg_shell.c
index 73d9477f..412488b3 100644
--- a/sway/desktop/xdg_shell.c
+++ b/sway/desktop/xdg_shell.c
@@ -87,7 +87,7 @@ static const char *get_string_prop(struct sway_view *view, enum sway_view_prop p
 	}
 }
 
-static void configure(struct sway_view *view, double ox, double oy, int width,
+static void configure(struct sway_view *view, double lx, double ly, int width,
 		int height) {
 	struct sway_xdg_shell_view *xdg_shell_view =
 		xdg_shell_view_from_view(view);
@@ -98,7 +98,7 @@ static void configure(struct sway_view *view, double ox, double oy, int width,
 	xdg_shell_view->pending_width = width;
 	xdg_shell_view->pending_height = height;
 	wlr_xdg_toplevel_set_size(view->wlr_xdg_surface, width, height);
-	view_update_position(view, ox, oy);
+	view_update_position(view, lx, ly);
 }
 
 static void set_activated(struct sway_view *view, bool activated) {
diff --git a/sway/desktop/xdg_shell_v6.c b/sway/desktop/xdg_shell_v6.c
index 6c98744c..b3653913 100644
--- a/sway/desktop/xdg_shell_v6.c
+++ b/sway/desktop/xdg_shell_v6.c
@@ -86,7 +86,7 @@ static const char *get_string_prop(struct sway_view *view, enum sway_view_prop p
 	}
 }
 
-static void configure(struct sway_view *view, double ox, double oy, int width,
+static void configure(struct sway_view *view, double lx, double ly, int width,
 		int height) {
 	struct sway_xdg_shell_v6_view *xdg_shell_v6_view =
 		xdg_shell_v6_view_from_view(view);
@@ -97,7 +97,7 @@ static void configure(struct sway_view *view, double ox, double oy, int width,
 	xdg_shell_v6_view->pending_width = width;
 	xdg_shell_v6_view->pending_height = height;
 	wlr_xdg_toplevel_v6_set_size(view->wlr_xdg_surface_v6, width, height);
-	view_update_position(view, ox, oy);
+	view_update_position(view, lx, ly);
 }
 
 static void set_activated(struct sway_view *view, bool activated) {
diff --git a/sway/desktop/xwayland.c b/sway/desktop/xwayland.c
index 783868bc..fc488162 100644
--- a/sway/desktop/xwayland.c
+++ b/sway/desktop/xwayland.c
@@ -152,9 +152,7 @@ static uint32_t get_int_prop(struct sway_view *view, enum sway_view_prop prop) {
 	}
 }
 
-// The x and y arguments are output-local for tiled views, and layout
-// coordinates for floating views.
-static void configure(struct sway_view *view, double x, double y, int width,
+static void configure(struct sway_view *view, double lx, double ly, int width,
 		int height) {
 	struct sway_xwayland_view *xwayland_view = xwayland_view_from_view(view);
 	if (xwayland_view == NULL) {
@@ -162,30 +160,6 @@ static void configure(struct sway_view *view, double x, double y, int width,
 	}
 	struct wlr_xwayland_surface *xsurface = view->wlr_xwayland_surface;
 
-	double lx, ly;
-	if (container_is_floating(view->swayc)) {
-		lx = x;
-		ly = y;
-	} else {
-		struct sway_container *output = container_parent(view->swayc, C_OUTPUT);
-		if (!sway_assert(output, "view must be within tree to set position")) {
-			return;
-		}
-		struct sway_container *root = container_parent(output, C_ROOT);
-		if (!sway_assert(root, "output must be within tree to set position")) {
-			return;
-		}
-		struct wlr_output_layout *layout = root->sway_root->output_layout;
-		struct wlr_output_layout_output *loutput =
-			wlr_output_layout_get(layout, output->sway_output->wlr_output);
-		if (!sway_assert(loutput,
-					"output must be within layout to set position")) {
-			return;
-		}
-		lx = x + loutput->x;
-		ly = y + loutput->y;
-	}
-
 	xwayland_view->pending_width = width;
 	xwayland_view->pending_height = height;
 	wlr_xwayland_surface_configure(xsurface, lx, ly, width, height);
diff --git a/sway/input/cursor.c b/sway/input/cursor.c
index 96bf574c..16e5427b 100644
--- a/sway/input/cursor.c
+++ b/sway/input/cursor.c
@@ -46,7 +46,7 @@ static struct wlr_surface *layer_surface_at(struct sway_output *output,
  * location, it is stored in **surface (it may not be a view).
  */
 static struct sway_container *container_at_coords(
-		struct sway_seat *seat, double x, double y,
+		struct sway_seat *seat, double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
 	// check for unmanaged views first
 	struct wl_list *unmanaged = &root_container.sway_root->xwayland_unmanaged;
@@ -55,8 +55,8 @@ static struct sway_container *container_at_coords(
 		struct wlr_xwayland_surface *xsurface =
 			unmanaged_surface->wlr_xwayland_surface;
 
-		double _sx = x - unmanaged_surface->lx;
-		double _sy = y - unmanaged_surface->ly;
+		double _sx = lx - unmanaged_surface->lx;
+		double _sy = ly - unmanaged_surface->ly;
 		if (wlr_surface_point_accepts_input(xsurface->surface, _sx, _sy)) {
 			*surface = xsurface->surface;
 			*sx = _sx;
@@ -69,12 +69,12 @@ static struct sway_container *container_at_coords(
 	struct wlr_output_layout *output_layout =
 		root_container.sway_root->output_layout;
 	struct wlr_output *wlr_output = wlr_output_layout_output_at(
-			output_layout, x, y);
+			output_layout, lx, ly);
 	if (wlr_output == NULL) {
 		return NULL;
 	}
 	struct sway_output *output = wlr_output->data;
-	double ox = x, oy = y;
+	double ox = lx, oy = ly;
 	wlr_output_layout_output_coords(output_layout, wlr_output, &ox, &oy);
 
 	// find the focused workspace on the output for this seat
@@ -108,10 +108,10 @@ static struct sway_container *container_at_coords(
 	}
 
 	struct sway_container *c;
-	if ((c = floating_container_at(x, y, surface, sx, sy))) {
+	if ((c = floating_container_at(lx, ly, surface, sx, sy))) {
 		return c;
 	}
-	if ((c = container_at(ws, ox, oy, surface, sx, sy))) {
+	if ((c = container_at(ws, lx, ly, surface, sx, sy))) {
 		return c;
 	}
 
diff --git a/sway/tree/arrange.c b/sway/tree/arrange.c
index da4f7889..721b557e 100644
--- a/sway/tree/arrange.c
+++ b/sway/tree/arrange.c
@@ -73,8 +73,8 @@ void arrange_workspace(struct sway_container *workspace) {
 			area->width, area->height, area->x, area->y);
 	workspace->width = area->width;
 	workspace->height = area->height;
-	workspace->x = area->x;
-	workspace->y = area->y;
+	workspace->x = output->x + area->x;
+	workspace->y = output->y + area->y;
 	wlr_log(L_DEBUG, "Arranging workspace '%s' at %f, %f",
 			workspace->name, workspace->x, workspace->y);
 	arrange_children_of(workspace);
diff --git a/sway/tree/container.c b/sway/tree/container.c
index 12f74e37..7928ffc3 100644
--- a/sway/tree/container.c
+++ b/sway/tree/container.c
@@ -467,14 +467,14 @@ struct sway_container *container_parent(struct sway_container *container,
 }
 
 static struct sway_container *container_at_view(struct sway_container *swayc,
-		double ox, double oy,
+		double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
 	if (!sway_assert(swayc->type == C_VIEW, "Expected a view")) {
 		return NULL;
 	}
 	struct sway_view *sview = swayc->sway_view;
-	double view_sx = ox - sview->x;
-	double view_sy = oy - sview->y;
+	double view_sx = lx - sview->x;
+	double view_sy = ly - sview->y;
 
 	double _sx, _sy;
 	struct wlr_surface *_surface = NULL;
@@ -516,18 +516,18 @@ static struct sway_container *container_at_view(struct sway_container *swayc,
  * container_at for a container with layout L_TABBED.
  */
 static struct sway_container *container_at_tabbed(struct sway_container *parent,
-		double ox, double oy,
+		double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
-	if (oy < parent->y || oy > parent->y + parent->height) {
+	if (ly < parent->y || ly > parent->y + parent->height) {
 		return NULL;
 	}
 	struct sway_seat *seat = input_manager_current_seat(input_manager);
 
 	// Tab titles
 	int title_height = container_titlebar_height();
-	if (oy < parent->y + title_height) {
+	if (ly < parent->y + title_height) {
 		int tab_width = parent->width / parent->children->length;
-		int child_index = (ox - parent->x) / tab_width;
+		int child_index = (lx - parent->x) / tab_width;
 		if (child_index >= parent->children->length) {
 			child_index = parent->children->length - 1;
 		}
@@ -538,23 +538,23 @@ static struct sway_container *container_at_tabbed(struct sway_container *parent,
 	// Surfaces
 	struct sway_container *current = seat_get_active_child(seat, parent);
 
-	return container_at(current, ox, oy, surface, sx, sy);
+	return container_at(current, lx, ly, surface, sx, sy);
 }
 
 /**
  * container_at for a container with layout L_STACKED.
  */
 static struct sway_container *container_at_stacked(
-		struct sway_container *parent, double ox, double oy,
+		struct sway_container *parent, double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
-	if (oy < parent->y || oy > parent->y + parent->height) {
+	if (ly < parent->y || ly > parent->y + parent->height) {
 		return NULL;
 	}
 	struct sway_seat *seat = input_manager_current_seat(input_manager);
 
 	// Title bars
 	int title_height = container_titlebar_height();
-	int child_index = (oy - parent->y) / title_height;
+	int child_index = (ly - parent->y) / title_height;
 	if (child_index < parent->children->length) {
 		struct sway_container *child = parent->children->items[child_index];
 		return seat_get_focus_inactive(seat, child);
@@ -563,14 +563,14 @@ static struct sway_container *container_at_stacked(
 	// Surfaces
 	struct sway_container *current = seat_get_active_child(seat, parent);
 
-	return container_at(current, ox, oy, surface, sx, sy);
+	return container_at(current, lx, ly, surface, sx, sy);
 }
 
 /**
  * container_at for a container with layout L_HORIZ or L_VERT.
  */
 static struct sway_container *container_at_linear(struct sway_container *parent,
-		double ox, double oy,
+		double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
 	for (int i = 0; i < parent->children->length; ++i) {
 		struct sway_container *child = parent->children->items[i];
@@ -580,22 +580,22 @@ static struct sway_container *container_at_linear(struct sway_container *parent,
 			.width = child->width,
 			.height = child->height,
 		};
-		if (wlr_box_contains_point(&box, ox, oy)) {
-			return container_at(child, ox, oy, surface, sx, sy);
+		if (wlr_box_contains_point(&box, lx, ly)) {
+			return container_at(child, lx, ly, surface, sx, sy);
 		}
 	}
 	return NULL;
 }
 
 struct sway_container *container_at(struct sway_container *parent,
-		double ox, double oy,
+		double lx, double ly,
 		struct wlr_surface **surface, double *sx, double *sy) {
 	if (!sway_assert(parent->type >= C_WORKSPACE,
 				"Expected workspace or deeper")) {
 		return NULL;
 	}
 	if (parent->type == C_VIEW) {
-		return container_at_view(parent, ox, oy, surface, sx, sy);
+		return container_at_view(parent, lx, ly, surface, sx, sy);
 	}
 	if (!parent->children->length) {
 		return NULL;
@@ -604,11 +604,11 @@ struct sway_container *container_at(struct sway_container *parent,
 	switch (parent->layout) {
 	case L_HORIZ:
 	case L_VERT:
-		return container_at_linear(parent, ox, oy, surface, sx, sy);
+		return container_at_linear(parent, lx, ly, surface, sx, sy);
 	case L_TABBED:
-		return container_at_tabbed(parent, ox, oy, surface, sx, sy);
+		return container_at_tabbed(parent, lx, ly, surface, sx, sy);
 	case L_STACKED:
-		return container_at_stacked(parent, ox, oy, surface, sx, sy);
+		return container_at_stacked(parent, lx, ly, surface, sx, sy);
 	case L_FLOATING:
 		sway_assert(false, "Didn't expect to see floating here");
 		return NULL;
@@ -837,7 +837,7 @@ static size_t get_tree_representation(struct sway_container *parent, char *buffe
 		lenient_strcat(buffer, "S[");
 		break;
 	case L_FLOATING:
-		strcpy(buffer, "F[");
+		lenient_strcat(buffer, "F[");
 		break;
 	case L_NONE:
 		lenient_strcat(buffer, "D[");
diff --git a/sway/tree/view.c b/sway/tree/view.c
index 3de9879e..065d00db 100644
--- a/sway/tree/view.c
+++ b/sway/tree/view.c
@@ -119,10 +119,10 @@ const char *view_get_shell(struct sway_view *view) {
 	return "unknown";
 }
 
-void view_configure(struct sway_view *view, double ox, double oy, int width,
+void view_configure(struct sway_view *view, double lx, double ly, int width,
 		int height) {
 	if (view->impl->configure) {
-		view->impl->configure(view, ox, oy, width, height);
+		view->impl->configure(view, lx, ly, width, height);
 	}
 }
 
@@ -134,9 +134,8 @@ static void view_autoconfigure_floating(struct sway_view *view) {
 		view->natural_width > max_width ? max_width : view->natural_width;
 	int height =
 		view->natural_height > max_height ? max_height : view->natural_height;
-	struct sway_container *output = ws->parent;
-	int lx = output->x + (ws->width - width) / 2;
-	int ly = output->y + (ws->height - height) / 2;
+	int lx = ws->x + (ws->width - width) / 2;
+	int ly = ws->y + (ws->height - height) / 2;
 
 	view->border_left = view->border_right = view->border_bottom = true;
 	view_set_tiled(view, false);
@@ -152,8 +151,7 @@ void view_autoconfigure(struct sway_view *view) {
 	struct sway_container *output = container_parent(view->swayc, C_OUTPUT);
 
 	if (view->is_fullscreen) {
-		view_configure(view, 0, 0, output->width, output->height);
-		view->x = view->y = 0;
+		view_configure(view, output->x, output->y, output->width, output->height);
 		return;
 	}
 
@@ -560,6 +558,9 @@ void view_unmap(struct sway_view *view) {
 }
 
 void view_update_position(struct sway_view *view, double lx, double ly) {
+	if (view->x == lx && view->y == ly) {
+		return;
+	}
 	if (!container_is_floating(view->swayc)) {
 		return;
 	}