diff --git a/merge/box.go b/merge/box.go
index 633cd88..674bd1d 100644
--- a/merge/box.go
+++ b/merge/box.go
@@ -11,6 +11,7 @@ import (
 // heterogeneous members, but should likely be avoided otherwise.
 type Boxed struct {
 	val   interface{}
+	ident func() interface{}
 	merge func(interface{}) error
 }
 
@@ -21,8 +22,18 @@ func (b Boxed) Merge(from Boxed) error {
 	return nil
 }
 
+func (b Boxed) MergeIdentity() Boxed {
+	return Boxed{
+		val: b.ident(),
+		ident: b.ident,
+		merge: b.merge,
+	}
+}
+
 var typeMismatch = errors.New("mismatched types")
 
+// strip takes a typed function and erases the type information from its
+// parameter
 func strip[X any](f func(X) error) func(interface{}) error {
 	return func(v interface{}) error {
 		vv, ok := v.(X)
@@ -38,6 +49,9 @@ func strip[X any](f func(X) error) func(interface{}) error {
 func Box[X Merges[X]](x X) Boxed {
 	return Boxed{
 		val: x,
+		ident: func() interface{} {
+			return x.MergeIdentity()
+		},
 		merge: strip(x.Merge),
 	}
 }
diff --git a/merge/merge.go b/merge/merge.go
index 08fdf48..b3ecd18 100644
--- a/merge/merge.go
+++ b/merge/merge.go
@@ -18,6 +18,7 @@ package merge
 // Although the type B satisfies the interface Merges[*C], it does not satisfy
 // the constraint [X Merges[X]], which is what is used throughout this package.
 type Merges[X any] interface {
+	MergeIdentity() X
 	Merge(X) error
 }
 
diff --git a/merge/merge_test.go b/merge/merge_test.go
index fe5d2d9..04be542 100644
--- a/merge/merge_test.go
+++ b/merge/merge_test.go
@@ -10,6 +10,10 @@ type additive struct {
 	total int
 }
 
+func (*additive) MergeIdentity() *additive {
+	return new(additive)
+}
+
 func (a *additive) Merge(b *additive) error {
 	a.total += b.total
 	return nil
@@ -23,6 +27,10 @@ type multiplicative struct {
 	scale int
 }
 
+func (m *multiplicative) MergeIdentity() *multiplicative {
+	return &multiplicative{scale: 1}
+}
+
 func (m *multiplicative) Merge(v *multiplicative) error {
 	m.scale *= v.scale
 	return nil
@@ -38,6 +46,8 @@ type exclusive struct {
 	stock int
 }
 
+func (*exclusive) MergeIdentity() *exclusive { return new(exclusive) }
+
 func (e *exclusive) Merge(source *exclusive) error {
 	e.stock += source.stock
 	source.stock = 0
@@ -75,5 +85,3 @@ func TestMerge(t *testing.T) {
 		}
 	})
 }
-
-
diff --git a/merge/table.go b/merge/table.go
index 609b553..8f43c35 100644
--- a/merge/table.go
+++ b/merge/table.go
@@ -10,7 +10,12 @@ func (t Table[K, V]) Merge(from Table[K, V]) error {
 	for k, v := range from {
 		e, ok := t[k]
 		if !ok {
-			t[k] = v
+			var z V
+			z = z.MergeIdentity()
+			if err := z.Merge(v); err != nil {
+				return fmt.Errorf("tables failed to merge: %w", err)
+			}
+			t[k] = z
 			continue
 		}
 
diff --git a/merge/table_test.go b/merge/table_test.go
index cb1affd..419e0e9 100644
--- a/merge/table_test.go
+++ b/merge/table_test.go
@@ -35,4 +35,7 @@ func TestMergeTables(t *testing.T) {
 	check("strawberry", 2)
 	check("pistacchio", 5)
 
+	bob["pistacchio"].Merge(add(100))
+	bob["pistacchio"] = add(1)
+	check("pistacchio", 5)
 }