diff --git a/acedoc.go b/acedoc.go
index 2de1e4e..3f4811b 100644
--- a/acedoc.go
+++ b/acedoc.go
@@ -74,8 +74,11 @@ func (d Delta) rows() int {
 }
 
 func (d Delta) cols() int {
-	r := int(d.End.Column) - int(d.Start.Column)
-	return r
+	if d.Start.Row == d.End.Row {
+		return int(d.End.Column) - int(d.Start.Column)
+	} else {
+		return int(d.End.Column)
+	}
 }
 
 func (d *Document) Contents() string {
diff --git a/delta.go b/delta.go
index 0076199..b67de9b 100644
--- a/delta.go
+++ b/delta.go
@@ -112,24 +112,33 @@ func (d Delta) Equal(other Delta) bool {
 }
 
 func Remove(row, col uint, str string) Delta {
-	lines := strings.Split(str, "\n")
-	nlines := len(lines) - 1
-	return Delta{
-		Action: DeltaRemove,
-		Lines:  lines,
-		Start:  Position{row, col},
-		End:    Position{row + uint(nlines), uint(len(lines[nlines]))},
-	}
+	dl := Insert(row, col, str)
+	dl.Action = DeltaRemove
+	return dl
 }
 
 func Insert(row, col uint, str string) Delta {
 	lines := strings.Split(str, "\n")
-	nlines := uint(len(lines) - 1)
+
+	var endcol uint
+	addedLines := uint(len(lines) - 1)
+
+	if len(lines) == 0 {
+		addedLines = 1
+	} else {
+		lastLine := lines[len(lines)-1]
+		endcol += uint(len(lastLine))
+	}
+
+	if addedLines == 0 {
+		endcol += col
+	}
+
 	return Delta{
 		Action: DeltaInsert,
 		Lines:  lines,
 		Start:  Position{row, col},
-		End:    Position{row + nlines, uint(len(lines[nlines]))},
+		End:    Position{row + addedLines, endcol},
 	}
 }
 
@@ -215,7 +224,7 @@ func (d *Document) validate(dl Delta) error {
 	}
 
 	if dl.Action == DeltaRemove && !d.InDocument(dl.End) {
-		return fmt.Errorf("end is not in document for remove")
+		return fmt.Errorf("end %v is not in document %q for remove", dl.End, d.contents())
 	}
 
 	if dl.nLines() != dl.nRows() {