diff --git a/ts/a11y/explorer/KeyExplorer.ts b/ts/a11y/explorer/KeyExplorer.ts
index b62cf780a..d9b7fb3ec 100644
--- a/ts/a11y/explorer/KeyExplorer.ts
+++ b/ts/a11y/explorer/KeyExplorer.ts
@@ -223,6 +223,13 @@ export class SpeechExplorer
       creating an SVG version of the expression, and viewing various other
       information.</p>
 
+      <p>Finally, selecting the "Insert Hidden MathML" item from the options
+      submenu will turn of MathJax's speech and Braille generation and
+      instead use visually hidden MathML that some screen readers can voice,
+      though support for this is not universal across all screen readers and
+      operating systems.  Selecting speech or Braille generation in their
+      submenus will remove the hidden MathML again.</p>
+
       <p>For more help, see the <a
       href="https://docs.mathjax.org/en/latest/basic/accessibility.html"
       target="_blank">MathJax accessibility documentation.</a></p>
diff --git a/ts/ui/menu/Menu.ts b/ts/ui/menu/Menu.ts
index fa8dd9d4d..acfeec0fc 100644
--- a/ts/ui/menu/Menu.ts
+++ b/ts/ui/menu/Menu.ts
@@ -1203,6 +1203,16 @@ export class Menu {
    */
   protected setAssistiveMml(mml: boolean) {
     this.document.options.enableAssistiveMml = mml;
+    if (mml) {
+      this.noRerender(() => {
+        if (this.settings.speech) {
+          this.menu.pool.lookup('speech').setValue(false);
+        }
+        if (this.settings.braille) {
+          this.menu.pool.lookup('braille').setValue(false);
+        }
+      });
+    }
     if (!mml || MathJax._?.a11y?.['assistive-mml']) {
       this.rerender();
     } else {
@@ -1236,6 +1246,11 @@ export class Menu {
   protected setSpeech(speech: boolean) {
     this.enableAccessibilityItems('Speech', speech);
     this.document.options.enableSpeech = speech;
+    if (speech && this.settings.assistiveMml) {
+      this.noRerender(() =>
+        this.menu.pool.lookup('assistiveMml').setValue(false)
+      );
+    }
     if (!speech || MathJax._?.a11y?.explorer) {
       this.rerender(STATE.COMPILED);
     } else {
@@ -1249,6 +1264,11 @@ export class Menu {
   protected setBraille(braille: boolean) {
     this.enableAccessibilityItems('Braille', braille);
     this.document.options.enableBraille = braille;
+    if (braille && this.settings.assistiveMml) {
+      this.noRerender(() =>
+        this.menu.pool.lookup('assistiveMml').setValue(false)
+      );
+    }
     if (!braille || MathJax._?.a11y?.explorer) {
       this.rerender(STATE.COMPILED);
     } else {
@@ -1381,24 +1401,24 @@ export class Menu {
    * Reset all menu settings to the (page) defaults
    */
   protected resetDefaults() {
-    Menu.loading++; // pretend we're loading, to suppress rerendering for each variable change
-    const pool = this.menu.pool;
-    const settings = this.defaultSettings;
-    for (const name of Object.keys(settings) as (keyof MenuSettings)[]) {
-      const variable = pool.lookup(name);
-      if (variable) {
-        if (variable.getValue() !== settings[name]) {
-          variable.setValue(settings[name] as string | boolean);
-          const item = (variable as any).items[0];
-          if (item) {
-            item.executeCallbacks_();
+    this.noRerender(() => {
+      const pool = this.menu.pool;
+      const settings = this.defaultSettings;
+      for (const name of Object.keys(settings) as (keyof MenuSettings)[]) {
+        const variable = pool.lookup(name);
+        if (variable) {
+          if (variable.getValue() !== settings[name]) {
+            variable.setValue(settings[name] as string | boolean);
+            const item = (variable as any).items[0];
+            if (item) {
+              item.executeCallbacks_();
+            }
           }
+        } else if (Object.hasOwn(this.settings, name)) {
+          (this.settings as any)[name] = settings[name];
         }
-      } else if (Object.hasOwn(this.settings, name)) {
-        (this.settings as any)[name] = settings[name];
       }
-    }
-    Menu.loading--;
+    });
     this.rerender(STATE.COMPILED);
   }
 
@@ -1694,6 +1714,17 @@ export class Menu {
     }
   }
 
+  protected noRerender(exec: () => void) {
+    Menu.loading++; // pretend we're loading, to suppress rerendering durring exec() call
+    try {
+      exec();
+      Menu.loading--;
+    } catch (err) {
+      Menu.loading--; // make sure this resets if there is an error
+      throw err;
+    }
+  }
+
   /**
    * Copy the serialzied MathML to the clipboard
    */