diff --git a/ast_tools/passes/ssa.py b/ast_tools/passes/ssa.py
index 97d8240..77ca468 100644
--- a/ast_tools/passes/ssa.py
+++ b/ast_tools/passes/ssa.py
@@ -62,6 +62,12 @@ def visit(self, node: ast.AST) -> ast.AST:
         else:
             return super().visit(node)
 
+    def visit_Assign(self, node):
+        # visit RHS first
+        node.value = self.visit(node.value)
+        node.targets = [self.visit(t) for t in node.targets]
+        return node
+
 
     def visit_If(self, node: ast.If) -> tp.List[ast.stmt]:
         test = self.visit(node.test)
@@ -209,8 +215,16 @@ def visit_Name(self, node: ast.Name) -> ast.Name:
         name = node.id
         ctx = node.ctx
         if isinstance(ctx, ast.Load):
+            # Names in Load context should not be added to the name table
+            # as it makes them seem like they have been modified.
+            try:
+                return ast.Name(
+                        id=self.name_table[name],
+                        ctx=ctx)
+            except KeyError:
+                pass
             return ast.Name(
-                    id=self.name_table.setdefault(name, name),
+                    id=name,
                     ctx=ctx)
         else:
             return ast.Name(
diff --git a/tests/test_ssa.py b/tests/test_ssa.py
index dd6bea3..89b8f74 100644
--- a/tests/test_ssa.py
+++ b/tests/test_ssa.py
@@ -1,4 +1,5 @@
 import ast
+import inspect
 
 import pytest
 
@@ -119,3 +120,57 @@ def test_imbalanced(a, b, c, d):
         for x in (False, True):
             for y in (False, True):
                 assert imbalanced(x, y) == imbalanced_ssa(x, y)
+
+
+def test_reassign_arg():
+    def bar(x):
+        return x
+
+    @end_rewrite()
+    @ssa()
+    @begin_rewrite()
+    def foo(a, b):
+        if b:
+            a = bar(a)
+        return a
+    assert inspect.getsource(foo) == """\
+def foo(a, b):
+    a0 = bar(a)
+    a1 = a0 if b else a
+    __return_value0 = a1
+    return __return_value0
+"""
+
+
+def test_double_nested_function_call():
+    def bar(x):
+        return x
+
+    def baz(x):
+        return x + 1
+
+    @end_rewrite()
+    @ssa()
+    @begin_rewrite()
+    def foo(a, b, c):
+        if b:
+            a = bar(a)
+        else:
+            a = bar(a)
+        if c:
+            b = bar(b)
+        else:
+            b = bar(b)
+        return a, b
+    print(inspect.getsource(foo))
+    assert inspect.getsource(foo) == """\
+def foo(a, b, c):
+    a0 = bar(a)
+    a1 = bar(a)
+    a2 = a0 if b else a1
+    b0 = bar(b)
+    b1 = bar(b)
+    b2 = b0 if c else b1
+    __return_value0 = a2, b2
+    return __return_value0
+"""