diff --git a/datatype.go b/datatype.go
index b8f4610..028cb65 100644
--- a/datatype.go
+++ b/datatype.go
@@ -157,37 +157,27 @@ func columnItems(n node) (items []*template, nullable bool) {
 	return items, nullable
 }
 
-// disagreement names the fix for two items of one column holding different datatypes.
+// disagreement names the fix for two items of one column holding different datatypes. The item to
+// fix declares none, and is text where the other reads a typed column.
 func disagreement(a *template, da DataType, b *template, db DataType) error {
-	bare, typed, want := b, a, da
-	if da == DataTypeString {
-		bare, typed, want = a, b, db
+	fix, has, other, want := a, da, b, db
+	if da != DataTypeString && (a.datatype != DataTypeString || db == DataTypeString) {
+		fix, has, other, want = b, db, a, da
 	}
+	proven := (&valueProof{}).proveColumnItem(fix).not[want] == ""
 	switch {
-	case da != DataTypeString && db != DataTypeString:
-		return bothTyped(a, da, b, db)
-	case typed.datatype == DataTypeString && (&valueProof{}).proveColumnItem(bare).not[want] != "":
-		return fmt.Errorf(`item %q is not %s, the datatype item %q takes from the column it reads; to read that column as text, %s`, bare.format, dataTypeNouns[want], typed.format, asText(typed))
-	case bare.fromString: // an object may carry a weight, which this spelling would drop
-		return fmt.Errorf(`item %q declares no datatype, and a column holds one; write it as {"format":%q,"datatype":%q}`, bare.format, bare.format, want)
-	}
-	return fmt.Errorf(`item %q declares no datatype beside one holding %s; a column holds one, so give it "datatype": %q`, bare.format, want, want)
-}
-
-// bothTyped names the fix for two items holding different datatypes: the one taking its datatype
-// from the column it reads is typed as the other where its values prove it, else read as text.
-func bothTyped(a *template, da DataType, b *template, db DataType) error {
-	read, other := a, db
-	if a.datatype != DataTypeString {
-		read, other = b, da
-	}
-	switch {
-	case read.datatype != DataTypeString:
+	case fix.datatype != DataTypeString:
 		return fmt.Errorf("its items hold %s and %s; a column holds one datatype", da, db)
-	case (&valueProof{}).proveColumnItem(read).not[other] == "":
-		return fmt.Errorf("its items hold %s and %s; a column holds one datatype, so %s", da, db, typedAs(read, other))
+	case has != DataTypeString && proven:
+		return fmt.Errorf("its items hold %s and %s; a column holds one datatype, so %s", da, db, typedAs(fix, want))
+	case has != DataTypeString:
+		return fmt.Errorf("its items hold %s and %s; a column holds one datatype, so to read %q as text, %s", da, db, fix.format, asText(fix))
+	case other.datatype == DataTypeString && !proven:
+		return fmt.Errorf(`item %q is not %s, the datatype item %q takes from the column it reads; to read that column as text, %s`, fix.format, dataTypeNouns[want], other.format, asText(other))
+	case fix.fromString: // an object may carry a weight, which this spelling would drop
+		return fmt.Errorf(`item %q declares no datatype, and a column holds one; write it as {"format":%q,"datatype":%q}`, fix.format, fix.format, want)
 	}
-	return fmt.Errorf("its items hold %s and %s; a column holds one datatype, so to read %q as text, %s", da, db, read.format, asText(read))
+	return fmt.Errorf(`item %q declares no datatype beside one holding %s; a column holds one, so give it "datatype": %q`, fix.format, want, want)
 }
 
 // typedAs names the spelling giving a column-read item datatype d, keeping the other keys an object
diff --git a/todo.md b/todo.md
index e9e2783..0a08c1e 100644
--- a/todo.md
+++ b/todo.md
@@ -21,8 +21,6 @@ Self-sufficiency 5.6), every seat capped by Locality, and all nine naming
 
 This round, in order:
 
-- Make `disagreement` and `bothTyped` a table of cases: each swaps its operands and
-  runs a proof to pick an error's wording.
 - Derive a column's datatype in one place: `columnItems` yields nothing for a
   `tableColumn`, and six callers re-derive it from items.
 - Give `head`, `index`, `bound` and `draw` one meaning each, name `table.family`