diff --git a/src/Grid.zig b/src/Grid.zig
index ad5ec0f92..0b72b2a2d 100644
--- a/src/Grid.zig
+++ b/src/Grid.zig
@@ -58,6 +58,9 @@ foreground: terminal.color.RGB,
 /// Default background color
 background: terminal.color.RGB,
 
+/// The current value of the Z buffer.
+cell_z: u16 = 0,
+
 /// Available cursor styles for drawing. The values represents the mode value
 /// in the shader.
 pub const CursorStyle = enum(u8) {
@@ -307,12 +310,18 @@ pub fn rebuildCells(self: *Grid, term: Terminal) !void {
     // We've written no data to the GPU, refresh it all
     self.gl_cells_written = 0;
 
+    // Reset the Z buffer at the end no matter what since we're fresh.
+    defer self.cell_z = 0;
+
     // Build each cell
     var rowIter = term.screen.rowIterator(.viewport);
     var y: usize = 0;
     while (rowIter.next()) |line| {
         defer y += 1;
-        for (line) |cell, x| assert(try self.updateCell(term, cell, x, y));
+        for (line) |cell, x| {
+            self.cell_z = 0;
+            assert(try self.updateCell(term, cell, x, y));
+        }
     }
 
     // Add the cursor
@@ -328,8 +337,10 @@ pub fn finalizeCells(self: *Grid, term: Terminal) !void {
     if (self.cells.items.len < self.cells.capacity)
         self.addCursor(term);
 
-    // If we're out of space, rebuild
-    if (self.cells.items.len == self.cells.capacity) {
+    // If we're out of space or we have no more Z-space, rebuild.
+    if (self.cells.items.len == self.cells.capacity or
+        self.cell_z == std.math.maxInt(@TypeOf(self.cell_z)))
+    {
         log.info("cell cache full, rebuilding from scratch", .{});
         try self.rebuildCells(term);
     }
@@ -434,13 +445,25 @@ pub fn updateCell(
     };
     if (self.cells.items.len + needed > self.cells.capacity) return false;
 
+    // Bump our Z value. The "zbump" is the max amount we could increase
+    // the Z value this call. If it could theoretically go over the max
+    // int size of the Z type, then we return false -- we need a rebuild.
+    const zbump = 2;
+    const zmax = std.math.maxInt(@TypeOf(self.cell_z));
+    const zmax_padded = zmax - (zbump * 2);
+    if (self.cell_z > zmax_padded) {
+        self.cell_z = zmax;
+        return false;
+    }
+    self.cell_z += zbump;
+
     // If the cell has a background, we always draw it.
     if (colors.bg) |rgb| {
         self.cells.appendAssumeCapacity(.{
             .mode = 1,
             .grid_col = @intCast(u16, x),
             .grid_row = @intCast(u16, y),
-            .grid_z = 0,
+            .grid_z = self.cell_z,
             .glyph_x = 0,
             .glyph_y = 0,
             .glyph_width = 0,
@@ -479,7 +502,7 @@ pub fn updateCell(
             .mode = 2,
             .grid_col = @intCast(u16, x),
             .grid_row = @intCast(u16, y),
-            .grid_z = 1,
+            .grid_z = self.cell_z + 1,
             .glyph_x = glyph.atlas_x,
             .glyph_y = glyph.atlas_y,
             .glyph_width = glyph.width,
@@ -502,7 +525,7 @@ pub fn updateCell(
             .mode = 6, // underline
             .grid_col = @intCast(u16, x),
             .grid_row = @intCast(u16, y),
-            .grid_z = 1,
+            .grid_z = self.cell_z + 1,
             .glyph_x = 0,
             .glyph_y = 0,
             .glyph_width = 0,