diff --git a/src/marks/arrow.d.ts b/src/marks/arrow.d.ts
index 2cbd0f3a58..4ecff4b87c 100644
--- a/src/marks/arrow.d.ts
+++ b/src/marks/arrow.d.ts
@@ -86,14 +86,15 @@ export interface ArrowOptions extends MarkOptions {
   insetEnd?: number;
 
   /**
-   * The sweep order; defaults to null. If set to order-x, the bend angle is
-   * flipped when the ending point is to the left of the starting point—ensuring
-   * all arrows bulge up (down if bend is negative). If set to order-y, the bend
-   * angle is flipped when the ending point is above the starting point—ensuring
-   * all arrows bulge right (left if bend is negative). If set to order, applies
-   * an order-x sweep, and breaks ties with order-y.
+   * The sweep order; defaults to 1 indicating a positive (clockwise) bend
+   * angle; -1 indicates a negative (anticlockwise) bend angle; 0 effectively
+   * clears the bend angle. If set to -x, the bend angle is flipped when the
+   * ending point is to the left of the starting point—ensuring all arrows bulge
+   * up (down if bend is negative); if set to -y, the bend angle is flipped when
+   * the ending point is above the starting point—ensuring all arrows bulge
+   * right (left if bend is negative); the sign is negated for +x and +y.
    */
-  sweep?: null | "order-x" | "order-y" | "order";
+  sweep?: number | "+x" | "-x" | "+y" | "-y" | ((x1: number, y1: number, x2: number, y2: number) => number);
 }
 
 /**
diff --git a/src/marks/arrow.js b/src/marks/arrow.js
index 43ba2dee5f..7d1bdaf217 100644
--- a/src/marks/arrow.js
+++ b/src/marks/arrow.js
@@ -1,4 +1,4 @@
-import {descending} from "d3";
+import {ascending, descending} from "d3";
 import {create} from "../context.js";
 import {Mark} from "../mark.js";
 import {radians} from "../math.js";
@@ -28,7 +28,7 @@ export class Arrow extends Mark {
       inset = 0,
       insetStart = inset,
       insetEnd = inset,
-      sweep = null
+      sweep
     } = options;
     super(
       data,
@@ -46,7 +46,7 @@ export class Arrow extends Mark {
     this.headLength = +headLength;
     this.insetStart = +insetStart;
     this.insetEnd = +insetEnd;
-    this.sweep = sweep == null ? sweep : keyword(sweep, "sweep", ["order-x", "order-y", "order"]);
+    this.sweep = maybeSweep(sweep);
   }
   render(index, scales, channels, dimensions, context) {
     const {x1: X1, y1: Y1, x2: X2 = X1, y2: Y2 = Y1, SW} = channels;
@@ -87,22 +87,12 @@ export class Arrow extends Mark {
             // wings, but that’s okay since vectors are usually small.)
             const headLength = Math.min(wingScale * sw(i), lineLength / 3);
 
-            // Maybe flip the bending, if a sweep order is applied.
-            const flip =
-              this.sweep == null
-                ? 1
-                : this.sweep === "order-x"
-                ? descending(x1, x2)
-                : this.sweep === "order-y"
-                ? descending(y1, y2)
-                : descending(x1, x2) || descending(y1, y2); // "order"
-
             // When bending, the offset between the straight line between the two points
             // and the outgoing tangent from the start point. (Also the negative
             // incoming tangent to the end point.) This must be within ±π/2. A positive
             // angle will produce a clockwise curve; a negative angle will produce a
             // counterclockwise curve; zero will produce a straight line.
-            const bendAngle = flip * bend * radians;
+            const bendAngle = this.sweep(x1, y1, x2, y2) * bend * radians;
 
             // The radius of the circle that intersects with the two endpoints
             // and has the specified bend angle.
@@ -164,6 +154,22 @@ export class Arrow extends Mark {
   }
 }
 
+// Maybe flip the bend angle, depending on the arrow orientation.
+function maybeSweep(sweep = 1) {
+  if (typeof sweep === "number") return constant(Math.sign(sweep));
+  if (typeof sweep === "function") return (x1, y1, x2, y2) => Math.sign(sweep(x1, y1, x2, y2));
+  switch (keyword(sweep, "sweep", ["+x", "-x", "+y", "-y"])) {
+    case "+x":
+      return (x1, y1, x2) => ascending(x1, x2);
+    case "-x":
+      return (x1, y1, x2) => descending(x1, x2);
+    case "+y":
+      return (x1, y1, x2, y2) => ascending(y1, y2);
+    case "-y":
+      return (x1, y1, x2, y2) => descending(y1, y2);
+  }
+}
+
 // Returns the center of a circle that goes through the two given points ⟨ax,ay⟩
 // and ⟨bx,by⟩ and has radius r. There are two such points; use the sign +1 or
 // -1 to choose between them. Returns [NaN, NaN] if r is too small.
diff --git a/test/plots/collatz.ts b/test/plots/collatz.ts
index 59c0f6c02b..277cf2ed77 100644
--- a/test/plots/collatz.ts
+++ b/test/plots/collatz.ts
@@ -46,7 +46,7 @@ export async function collatzArcDiagramUp() {
         dy: -3,
         bend: 70,
         inset: 4,
-        sweep: "order",
+        sweep: "-x",
         stroke: ([a, b]) => `url(#gradient${+(a > b)})`
       }),
       () =>
diff --git a/test/plots/miserables.ts b/test/plots/miserables.ts
index 72629f1a72..59e012bee0 100644
--- a/test/plots/miserables.ts
+++ b/test/plots/miserables.ts
@@ -37,7 +37,7 @@ export async function miserablesArcDiagram() {
         x: 0,
         y1: "source",
         y2: "target",
-        sweep: "order-y",
+        sweep: "-y",
         bend: 90,
         stroke: samegroup,
         sort: samegroup,