diff --git a/src/lint/collect-spelling-diagnostics.ts b/src/lint/collect-spelling-diagnostics.ts
index d6506948..245265a8 100644
--- a/src/lint/collect-spelling-diagnostics.ts
+++ b/src/lint/collect-spelling-diagnostics.ts
@@ -51,6 +51,10 @@ let matchers = [
     pattern: /\r/gu,
     message: 'Only Unix-style (LF) linebreaks are allowed',
   },
+  {
+    pattern: /(?<=\b[Ss]teps? )\d/gu,
+    message: 'Prefer using labeled steps and <emu-xref> tags over hardcoding step numbers',
+  },
 ];
 
 export function collectSpellingDiagnostics(sourceText: string) {
diff --git a/src/lint/rules/algorithm-step-numbering.ts b/src/lint/rules/algorithm-step-numbering.ts
index 69604252..4edf2faf 100644
--- a/src/lint/rules/algorithm-step-numbering.ts
+++ b/src/lint/rules/algorithm-step-numbering.ts
@@ -4,7 +4,7 @@ import type { LintingError } from '../algorithm-error-reporter-type';
 const ruleId = 'algorithm-step-numbering';
 
 /*
-Checks that step numbers are all `1`, with the exception of top-level lists whose first item is not `1`.
+Checks that step numbers are all `1`.
 */
 export default function (
   report: (e: LintingError) => void,
@@ -12,19 +12,9 @@ export default function (
   algorithmSource: string
 ): Observer {
   const nodeType = node.tagName;
-  let depth = -1;
-  let topLevelIsOne = false;
   return {
     enter(node: EcmarkdownNode) {
-      if (node.name === 'ol') {
-        ++depth;
-        if (depth === 0) {
-          topLevelIsOne = node.start === 1;
-        }
-      } else if (node.name === 'ordered-list-item') {
-        if (depth === 0 && !topLevelIsOne) {
-          return;
-        }
+      if (node.name === 'ordered-list-item') {
         let itemSource = algorithmSource.slice(
           node.location!.start.offset,
           node.location!.end.offset
@@ -41,10 +31,5 @@ export default function (
         }
       }
     },
-    exit(node: EcmarkdownNode) {
-      if (node.name === 'ol') {
-        --depth;
-      }
-    },
   };
 }
diff --git a/test/lint-algorithms.js b/test/lint-algorithms.js
index 9c7ff2ad..490a6180 100644
--- a/test/lint-algorithms.js
+++ b/test/lint-algorithms.js
@@ -121,6 +121,17 @@ describe('linting algorithms', function () {
     const ruleId = 'algorithm-step-numbering';
 
     it('simple', async function () {
+      await assertLint(
+        positioned`<emu-alg>
+          ${M}2. Step.
+          1. Step.
+        </emu-alg>`,
+        {
+          ruleId,
+          nodeType,
+          message: 'expected step number to be "1." (found "2.")',
+        }
+      );
       await assertLint(
         positioned`<emu-alg>
           1. Step.
@@ -161,7 +172,7 @@ describe('linting algorithms', function () {
 
       await assertLint(
         positioned`<emu-alg>
-          2. Step:
+          1. Step:
             ${M}2. Substep.
         </emu-alg>`,
         {
@@ -202,9 +213,9 @@ describe('linting algorithms', function () {
     it('negative', async function () {
       await assertLintFree(`
         <emu-alg>
-          2. Step.
-          3. Step.
-          40. Step.
+          1. Step.
+          1. Step.
+          1. Step.
         </emu-alg>
       `);
     });
diff --git a/test/lint-spelling.js b/test/lint-spelling.js
index 1d5e4287..77c5c2e1 100644
--- a/test/lint-spelling.js
+++ b/test/lint-spelling.js
@@ -171,6 +171,19 @@ windows:${M}\r
     );
   });
 
+  it('step numbers', async function () {
+    await assertLint(
+      positioned`
+        Something about step ${M}1.
+      `,
+      {
+        ruleId: 'spelling',
+        nodeType: 'text',
+        message: 'Prefer using labeled steps and <emu-xref> tags over hardcoding step numbers',
+      }
+    );
+  });
+
   it('negative', async function () {
     await assertLintFree(`
       <p>
@@ -188,6 +201,11 @@ windows:${M}\r
       <emu-clause id="example">
         <h1>Example</h1>
       </emu-clause>
+
+      <emu-alg>
+        1. [label="example-label"] Foo.
+      </emu-alg>
+      Something about step <emu-xref href="#step-example-label"></emu-xref>.
     `);
   });
 });