diff --git a/python/tskit/drawing.py b/python/tskit/drawing.py
index 840e6b208c..a158f0dfbe 100644
--- a/python/tskit/drawing.py
+++ b/python/tskit/drawing.py
@@ -194,8 +194,8 @@ def __init__(
         mutation_label_attrs=None,
         root_svg_attributes=None,
         style=None,
+        root_branch=None,
     ):
-        self.ts = ts
         if size is None:
             size = (200 * ts.num_trees, 200)
         if root_svg_attributes is None:
@@ -206,9 +206,15 @@ def __init__(
         self.drawing = svgwrite.Drawing(
             size=self.image_size, debug=True, **root_svg_attributes
         )
+        if node_labels is None:
+            node_labels = {u: str(u) for u in range(ts.num_nodes)}
         if style is not None:
             self.drawing.defs.add(self.drawing.style(style))
-        self.node_labels = {u: str(u) for u in range(ts.num_nodes)}
+        if root_branch is None:
+            root_branch = any(
+                any(tree.parent(mut.node) == NULL for mut in tree.mutations())
+                for tree in ts.trees()
+            )
         # TODO add general padding arguments following matplotlib's terminology.
         self.axes_x_offset = 15
         self.axes_y_offset = 10
@@ -231,6 +237,7 @@ def __init__(
                 node_label_attrs=node_label_attrs,
                 mutation_attrs=mutation_attrs,
                 mutation_label_attrs=mutation_label_attrs,
+                root_branch=root_branch,
             )
             for tree in ts.trees()
         ]
@@ -285,7 +292,7 @@ class SvgTree:
     """
     A class to draw a tree in SVG format.
 
-    See :meth:`Tree.draw_svg` for a description of usage and parameters.
+    See :meth:`Tree.draw_svg` for a description of usage and frequently used parameters.
     """
 
     def __init__(
@@ -303,6 +310,7 @@ def __init__(
         mutation_label_attrs=None,
         root_svg_attributes=None,
         style=None,
+        root_branch=None,
     ):
         self.tree = tree
         if size is None:
@@ -314,6 +322,10 @@ def __init__(
         self.drawing = self.setup_drawing()
         if style is not None:
             self.drawing.defs.add(self.drawing.style(style))
+        if root_branch is None:
+            # put a root branch in if we have mutations over the root
+            root_branch = any(tree.parent(mut.node) == NULL for mut in tree.mutations())
+        self.root_branch = root_branch
         self.treebox_x_offset = 10
         self.treebox_y_offset = 10
         self.treebox_width = size[0] - 2 * self.treebox_x_offset
@@ -434,13 +446,9 @@ def assign_y_coordinates(self, tree_height_scale, max_tree_height):
         # node labels within the treebox
         label_padding = 10
         y_padding = self.treebox_y_offset + 2 * label_padding
-        mutations_over_root = any(
-            any(tree.parent(mut.node) == NULL for mut in tree.mutations())
-            for tree in ts.trees()
-        )
         root_branch_length = 0
         height = self.image_size[1]
-        if mutations_over_root:
+        if self.root_branch:
             # Allocate a fixed about of space to show the mutations on the
             # 'root branch'
             root_branch_length = height / 10  # FIXME just draw branch??