diff --git a/include/sway/tree/container.h b/include/sway/tree/container.h
index 16a180f85..4d0e60031 100644
--- a/include/sway/tree/container.h
+++ b/include/sway/tree/container.h
@@ -322,12 +322,23 @@ void container_get_box(struct sway_container *container, struct wlr_box *box);
 void container_floating_translate(struct sway_container *con,
 		double x_amount, double y_amount);
 
+/**
+ * Choose an output for the floating container's new position.
+ */
+struct sway_container *container_floating_find_output(
+		struct sway_container *con);
+
 /**
  * Move a floating container to a new layout-local position.
  */
 void container_floating_move_to(struct sway_container *con,
 		double lx, double ly);
 
+/**
+ * Move a floating container to the center of the workspace.
+ */
+void container_floating_move_to_center(struct sway_container *con);
+
 /**
  * Mark a container as dirty if it isn't already. Dirty containers will be
  * included in the next transaction then unmarked as dirty.
diff --git a/include/sway/tree/workspace.h b/include/sway/tree/workspace.h
index 239cbbdb8..056f23299 100644
--- a/include/sway/tree/workspace.h
+++ b/include/sway/tree/workspace.h
@@ -16,6 +16,8 @@ struct sway_workspace {
 
 extern char *prev_workspace_name;
 
+struct sway_container *workspace_get_initial_output(const char *name);
+
 char *workspace_next_name(const char *output_name);
 
 bool workspace_switch(struct sway_container *workspace,
diff --git a/sway/commands/move.c b/sway/commands/move.c
index 95dcb0886..de6b1b0a4 100644
--- a/sway/commands/move.c
+++ b/sway/commands/move.c
@@ -100,7 +100,8 @@ static struct cmd_results *cmd_move_container(struct sway_container *current,
 	// determine destination
 	if (strcasecmp(argv[1], "workspace") == 0) {
 		// move container to workspace x
-		struct sway_container *ws;
+		struct sway_container *ws = NULL;
+		char *ws_name = NULL;
 		if (strcasecmp(argv[2], "next") == 0 ||
 				strcasecmp(argv[2], "prev") == 0 ||
 				strcasecmp(argv[2], "next_on_output") == 0 ||
@@ -110,14 +111,13 @@ static struct cmd_results *cmd_move_container(struct sway_container *current,
 		} else if (strcasecmp(argv[2], "back_and_forth") == 0) {
 			if (!(ws = workspace_by_name(argv[2]))) {
 				if (prev_workspace_name) {
-					ws = workspace_create(NULL, prev_workspace_name);
+					ws_name = strdup(prev_workspace_name);
 				} else {
 					return cmd_results_new(CMD_FAILURE, "move",
 							"No workspace was previously active.");
 				}
 			}
 		} else {
-			char *ws_name = NULL;
 			if (strcasecmp(argv[2], "number") == 0) {
 				// move "container to workspace number x"
 				if (argc < 4) {
@@ -141,12 +141,26 @@ static struct cmd_results *cmd_move_container(struct sway_container *current,
 					ws = workspace_by_name(ws_name);
 				}
 			}
-
-			if (!ws) {
-				ws = workspace_create(NULL, ws_name);
-			}
-			free(ws_name);
 		}
+		if (!ws) {
+			// We have to create the workspace, but if the container is
+			// sticky and the workspace is going to be created on the same
+			// output, we'll bail out first.
+			if (container_is_floating(current) && current->is_sticky) {
+				struct sway_container *old_output =
+					container_parent(current, C_OUTPUT);
+				struct sway_container *new_output =
+					workspace_get_initial_output(ws_name);
+				if (old_output == new_output) {
+					free(ws_name);
+					return cmd_results_new(CMD_FAILURE, "move",
+							"Can't move sticky container to another workspace "
+							"on the same output");
+				}
+			}
+			ws = workspace_create(NULL, ws_name);
+		}
+		free(ws_name);
 		destination = seat_get_focus_inactive(config->handler_context.seat, ws);
 	} else if (strcasecmp(argv[1], "output") == 0) {
 		struct sway_container *source = container_parent(current, C_OUTPUT);
@@ -173,6 +187,16 @@ static struct cmd_results *cmd_move_container(struct sway_container *current,
 		return cmd_results_new(CMD_INVALID, "move", expected_syntax);
 	}
 
+	if (container_is_floating(current) && current->is_sticky) {
+		struct sway_container *old_output = container_parent(current, C_OUTPUT);
+		struct sway_container *new_output = destination->type == C_OUTPUT ?
+			destination : container_parent(destination, C_OUTPUT);
+		if (old_output == new_output) {
+			return cmd_results_new(CMD_FAILURE, "move", "Can't move sticky "
+					"container to another workspace on the same output");
+		}
+	}
+
 	// move container, arrange windows and return focus
 	container_move_to(current, destination);
 	struct sway_container *focus =
diff --git a/sway/input/seat.c b/sway/input/seat.c
index dd4d5c3bf..6dd7cf7de 100644
--- a/sway/input/seat.c
+++ b/sway/input/seat.c
@@ -717,12 +717,8 @@ void seat_set_focus_warp(struct sway_seat *seat,
 
 	// If we've focused a floating container, bring it to the front.
 	// We do this by putting it at the end of the floating list.
-	// This must happen for both the pending and current children lists.
 	if (container && container_is_floating(container)) {
 		list_move_to_end(container->parent->children, container);
-		if (container_has_ancestor(container, container->current.parent)) {
-			list_move_to_end(container->parent->current.children, container);
-		}
 	}
 
 	// clean up unfocused empty workspace on new output
diff --git a/sway/tree/container.c b/sway/tree/container.c
index 6da5ac3c3..4507655e3 100644
--- a/sway/tree/container.c
+++ b/sway/tree/container.c
@@ -1163,19 +1163,16 @@ void container_floating_translate(struct sway_container *con,
 		double x_amount, double y_amount) {
 	con->x += x_amount;
 	con->y += y_amount;
-	con->current.swayc_x += x_amount;
-	con->current.swayc_y += y_amount;
 	if (con->type == C_VIEW) {
 		con->sway_view->x += x_amount;
 		con->sway_view->y += y_amount;
-		con->current.view_x += x_amount;
-		con->current.view_y += y_amount;
 	} else {
 		for (int i = 0; i < con->children->length; ++i) {
 			struct sway_container *child = con->children->items[i];
 			container_floating_translate(child, x_amount, y_amount);
 		}
 	}
+	container_set_dirty(con);
 }
 
 /**
@@ -1185,7 +1182,7 @@ void container_floating_translate(struct sway_container *con,
  * one, otherwise we'll choose whichever output is closest to the container's
  * center.
  */
-static struct sway_container *container_floating_find_output(
+struct sway_container *container_floating_find_output(
 		struct sway_container *con) {
 	double center_x = con->x + con->width / 2;
 	double center_y = con->y + con->height / 2;
@@ -1219,9 +1216,7 @@ void container_floating_move_to(struct sway_container *con,
 			"Expected a floating container")) {
 		return;
 	}
-	desktop_damage_whole_container(con);
 	container_floating_translate(con, lx - con->x, ly - con->y);
-	desktop_damage_whole_container(con);
 	struct sway_container *old_workspace = container_parent(con, C_WORKSPACE);
 	struct sway_container *new_output = container_floating_find_output(con);
 	if (!sway_assert(new_output, "Unable to find any output")) {
@@ -1239,6 +1234,17 @@ void container_floating_move_to(struct sway_container *con,
 	}
 }
 
+void container_floating_move_to_center(struct sway_container *con) {
+	if (!sway_assert(container_is_floating(con),
+			"Expected a floating container")) {
+		return;
+	}
+	struct sway_container *ws = container_parent(con, C_WORKSPACE);
+	double new_lx = ws->x + (ws->width - con->width) / 2;
+	double new_ly = ws->y + (ws->height - con->height) / 2;
+	container_floating_translate(con, new_lx - con->x, new_ly - con->y);
+}
+
 void container_set_dirty(struct sway_container *container) {
 	if (container->dirty) {
 		return;
@@ -1318,6 +1324,11 @@ void container_set_fullscreen(struct sway_container *container, bool enable) {
 			container->y = container->saved_y;
 			container->width = container->saved_width;
 			container->height = container->saved_height;
+			struct sway_container *output =
+				container_floating_find_output(container);
+			if (!container_has_ancestor(container, output)) {
+				container_floating_move_to_center(container);
+			}
 		} else {
 			container->width = container->saved_width;
 			container->height = container->saved_height;
diff --git a/sway/tree/layout.c b/sway/tree/layout.c
index 208156542..38e14d00b 100644
--- a/sway/tree/layout.c
+++ b/sway/tree/layout.c
@@ -150,22 +150,44 @@ void container_move_to(struct sway_container *container,
 			|| container_has_ancestor(container, destination)) {
 		return;
 	}
+	struct sway_container *old_parent = NULL;
+	struct sway_container *new_parent = NULL;
 	if (container_is_floating(container)) {
-		// TODO
-		return;
-	}
-	struct sway_container *old_parent = container_remove_child(container);
-	container->width = container->height = 0;
-	container->saved_width = container->saved_height = 0;
-
-	struct sway_container *new_parent;
-
-	if (destination->type == C_VIEW) {
-		new_parent = container_add_sibling(destination, container);
+		// Resolve destination into a workspace
+		struct sway_container *new_ws = NULL;
+		if (destination->type == C_OUTPUT) {
+			new_ws = output_get_active_workspace(destination->sway_output);
+		} else if (destination->type == C_WORKSPACE) {
+			new_ws = destination;
+		} else {
+			new_ws = container_parent(destination, C_WORKSPACE);
+		}
+		if (!new_ws) {
+			// This can happen if the user has run "move container to mark foo",
+			// where mark foo is on a hidden scratchpad container.
+			return;
+		}
+		struct sway_container *old_output =
+			container_parent(container, C_OUTPUT);
+		old_parent = container_remove_child(container);
+		container_add_child(new_ws->sway_workspace->floating, container);
+		// If changing output, center it within the workspace
+		if (old_output != new_ws->parent && !container->is_fullscreen) {
+			container_floating_move_to_center(container);
+		}
 	} else {
-		new_parent = destination;
-		container_add_child(destination, container);
+		old_parent = container_remove_child(container);
+		container->width = container->height = 0;
+		container->saved_width = container->saved_height = 0;
+
+		if (destination->type == C_VIEW) {
+			new_parent = container_add_sibling(destination, container);
+		} else {
+			new_parent = destination;
+			container_add_child(destination, container);
+		}
 	}
+
 	wl_signal_emit(&container->events.reparent, old_parent);
 
 	if (container->type == C_VIEW) {
diff --git a/sway/tree/workspace.c b/sway/tree/workspace.c
index 395c6c10c..b8bec044a 100644
--- a/sway/tree/workspace.c
+++ b/sway/tree/workspace.c
@@ -18,7 +18,7 @@
 #include "log.h"
 #include "util.h"
 
-static struct sway_container *get_workspace_initial_output(const char *name) {
+struct sway_container *workspace_get_initial_output(const char *name) {
 	struct sway_container *parent;
 	// Search for workspace<->output pair
 	int e = config->workspace_outputs->length;
@@ -48,7 +48,7 @@ static struct sway_container *get_workspace_initial_output(const char *name) {
 struct sway_container *workspace_create(struct sway_container *output,
 		const char *name) {
 	if (output == NULL) {
-		output = get_workspace_initial_output(name);
+		output = workspace_get_initial_output(name);
 	}
 
 	wlr_log(WLR_DEBUG, "Added workspace %s for output %s", name, output->name);