diff --git a/datatype.go b/datatype.go
index 80e1ede..5d2cc13 100644
--- a/datatype.go
+++ b/datatype.go
@@ -82,8 +82,14 @@ func checkColumns(s nodeScope) error {
 				}
 			}
 		}
-		if _, err := columnDatatype(column); err != nil {
-			return fmt.Errorf("%s: field %q: %w", path, name, err)
+		if len(items) == 0 {
+			return nil
+		}
+		first := itemDatatype(items[0])
+		for _, it := range items[1:] {
+			if d := itemDatatype(it); d != first {
+				return fmt.Errorf("%s: field %q: %w", path, name, disagreement(items[0], first, it, d))
+			}
 		}
 		return nil
 	}
@@ -101,41 +107,22 @@ func checkColumns(s nodeScope) error {
 	})
 }
 
-// columnDatatype is the datatype a column's items hold. They must agree, since a
-// column holds one; a column only ever null is a string.
-func columnDatatype(n node) (DataType, error) {
+// columnDatatype is the datatype a column holds, which its first item decides: checkColumns refuses
+// a column whose items disagree. A table's column, like one only ever null, has no item and is a string.
+func columnDatatype(n node) DataType {
 	items, _ := columnItems(n)
 	if len(items) == 0 {
-		return DataTypeString, nil
+		return DataTypeString
 	}
-	first := itemDatatype(items[0])
-	for _, t := range items[1:] {
-		if d := itemDatatype(t); d != first {
-			return first, disagreement(items[0], first, t, d)
-		}
-	}
-	return first, nil
+	return itemDatatype(items[0])
 }
 
-// itemDatatype is the datatype a column item declares, else that of the column it is.
+// itemDatatype is the datatype a column item declares, else that of the column it reads.
 func itemDatatype(t *template) DataType {
-	if t.datatype != DataTypeString {
-		return t.datatype
+	if t.datatype == DataTypeString && t.readsColumn != nil {
+		return columnDatatype(t.readsColumn.column)
 	}
-	return readDatatype(t)
-}
-
-// readDatatype is the datatype of the column t is, reading it by one reference alone; a string
-// when t reads none.
-func readDatatype(t *template) DataType {
-	if t.readsColumn == nil {
-		return DataTypeString
-	}
-	items, _ := columnItems(t.readsColumn.column)
-	if len(items) == 0 {
-		return DataTypeString
-	}
-	return itemDatatype(items[0]) // checkColumns refuses that column where its items disagree
+	return t.datatype
 }
 
 // columnItems is a column's template items, its choices unwrapped, and whether one is null.
diff --git a/record.go b/record.go
index f8016bd..67ef410 100644
--- a/record.go
+++ b/record.go
@@ -254,8 +254,7 @@ func recordOf(n node) (*template, []Column, error) {
 	}
 	columns := make([]Column, len(names))
 	for i, name := range names {
-		datatype, _ := columnDatatype(t.fields[name]) // checkColumns refused items that disagree wherever DataType is read
-		columns[i] = Column{Name: name, DataType: datatype}
+		columns[i] = Column{Name: name, DataType: columnDatatype(t.fields[name])}
 	}
 	return t, columns, nil
 }
diff --git a/todo.md b/todo.md
index 0a08c1e..ce50901 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:
 
-- 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`
   for the root it returns, and replace the token kind bytes `'l'`, `'t'`, `'f'` and
   `'b'`, whose `'l'` means different things in `ftoken` and `formatToken`.
diff --git a/value.go b/value.go
index 32718e4..89de4d8 100644
--- a/value.go
+++ b/value.go
@@ -34,8 +34,8 @@ func (p *valueProof) checkDatatype(path string, n node) error {
 	if !ok || t.datatype == DataTypeString {
 		return nil
 	}
-	if d := readDatatype(t); d == t.datatype {
-		return fmt.Errorf(`%s: %s takes datatype %s from the column it reads; drop "datatype"`, path, t.format, d)
+	if r := t.readsColumn; r != nil && columnDatatype(r.column) == t.datatype {
+		return fmt.Errorf(`%s: %s takes datatype %s from the column it reads; drop "datatype"`, path, t.format, t.datatype)
 	}
 	if reason := p.proveColumnItem(t).not[t.datatype]; reason != "" {
 		return fmt.Errorf("%s: datatype %s: %s", path, t.datatype, reason)