diff --git a/addons/docs/src/mdx/__testfixtures__/story-args.output.snapshot b/addons/docs/src/mdx/__testfixtures__/story-args.output.snapshot
index 13976ae013d..04a4e851ad9 100644
--- a/addons/docs/src/mdx/__testfixtures__/story-args.output.snapshot
+++ b/addons/docs/src/mdx/__testfixtures__/story-args.output.snapshot
@@ -65,7 +65,7 @@ componentNotes.args = {
   a: 1,
   b: 2,
 };
-componentNotes.parameters = { storySource: { source: 'Template.bind({})' } };
+componentNotes.parameters = { storySource: { source: 'args => <Button>Component notes</Button>' } };
 
 const componentMeta = { title: 'Button', includeStories: ['componentNotes'] };
 
diff --git a/addons/docs/src/mdx/mdx-compiler-plugin.js b/addons/docs/src/mdx/mdx-compiler-plugin.js
index e1d06ac3b27..3d85b1d2a5e 100644
--- a/addons/docs/src/mdx/mdx-compiler-plugin.js
+++ b/addons/docs/src/mdx/mdx-compiler-plugin.js
@@ -71,6 +71,32 @@ function genImportStory(ast, storyDef, storyName, context) {
   };
 }
 
+function getBodyPart(bodyNode, context) {
+  const body = bodyNode.type === 'JSXExpressionContainer' ? bodyNode.expression : bodyNode;
+  let sourceBody = body;
+  if (
+    body.type === 'CallExpression' &&
+    body.callee.type === 'MemberExpression' &&
+    body.callee.object.type === 'Identifier' &&
+    body.callee.property.type === 'Identifier' &&
+    body.callee.property.name === 'bind' &&
+    (body.arguments.length === 0 ||
+      (body.arguments.length === 1 &&
+        body.arguments[0].type === 'ObjectExpression' &&
+        body.arguments[0].properties.length === 0))
+  ) {
+    const bound = body.callee.object.name;
+    const namedExport = context.namedExports[bound];
+    if (namedExport) {
+      sourceBody = namedExport;
+    }
+  }
+
+  const { code: storyCode } = generate(body, {});
+  const { code: sourceCode } = generate(sourceBody, {});
+  return { storyCode, sourceCode, body };
+}
+
 function genStoryExport(ast, context) {
   let storyName = getAttr(ast.openingElement, 'name');
   let storyId = getAttr(ast.openingElement, 'id');
@@ -96,30 +122,29 @@ function genStoryExport(ast, context) {
 
   const bodyNodes = ast.children.filter((n) => n.type !== 'JSXText');
   let storyCode = null;
+  let sourceCode = null;
   let storyVal = null;
   if (!bodyNodes.length) {
     // plain text node
     const { code } = generate(ast.children[0], {});
     storyCode = `'${code}'`;
+    sourceCode = storyCode;
     storyVal = `() => (
       ${storyCode}
     )`;
   } else {
-    const bodyParts = bodyNodes.map((bodyNode) => {
-      const body = bodyNode.type === 'JSXExpressionContainer' ? bodyNode.expression : bodyNode;
-      const { code } = generate(body, {});
-      return { code, body };
-    });
+    const bodyParts = bodyNodes.map((bodyNode) => getBodyPart(bodyNode, context));
     // if we have more than two children
     // 1. Add line breaks
     // 2. Enclose in <> ... </>
-    storyCode = bodyParts.map(({ code }) => code).join('\n');
+    storyCode = bodyParts.map(({ storyCode: code }) => code).join('\n');
+    sourceCode = bodyParts.map(({ sourceCode: code }) => code).join('\n');
     const storyReactCode = bodyParts.length > 1 ? `<>\n${storyCode}\n</>` : storyCode;
     // keep track if an indentifier or function call
     // avoid breaking change for 5.3
     const BIND_REGEX = /\.bind\(.*\)/;
-    if (bodyParts.length === 1 && BIND_REGEX.test(bodyParts[0].code)) {
-      storyVal = bodyParts[0].code;
+    if (bodyParts.length === 1 && BIND_REGEX.test(bodyParts[0].storyCode)) {
+      storyVal = bodyParts[0].storyCode;
     } else {
       switch (bodyParts.length === 1 && bodyParts[0].body.type) {
         // We don't know what type the identifier is, but this code
@@ -152,7 +177,7 @@ function genStoryExport(ast, context) {
 
   let parameters = getAttr(ast.openingElement, 'parameters');
   parameters = parameters && parameters.expression;
-  const source = jsStringEscape(storyCode);
+  const source = jsStringEscape(sourceCode);
   const sourceParam = `storySource: { source: '${source}' }`;
   if (parameters) {
     const { code: params } = generate(parameters, {});
@@ -252,10 +277,13 @@ function getExports(node, counter, options) {
 
       const canvasExports = genCanvasExports(ast, counter);
 
+      // We're overwriting the Canvas tag here with a version that
+      // has the `name` attribute (e.g. `<Story name="..." story={...} />`)
+      // even if the user didn't provide one. We need the name attribute when
+      // we render the node at runtime.
       const { code } = generate(ast, {});
       // eslint-disable-next-line no-param-reassign
       node.value = code;
-
       return { stories: canvasExports };
     }
     if (META_REGEX.exec(value)) {
@@ -300,8 +328,48 @@ const hasStoryChild = (node) => {
   return null;
 };
 
-function extractExports(node, options) {
-  node.children.forEach((child) => {
+const getMdxSource = (children) =>
+  encodeURI(
+    children
+      .map(
+        (el) =>
+          generate(el, {
+            quotes: 'double',
+          }).code
+      )
+      .join('\n')
+  );
+
+// Parse out the named exports from a node, where the key
+// is the variable name and the value is the AST of the
+// variable declaration initializer
+const getNamedExports = (node) => {
+  const namedExports = {};
+  const ast = parser.parse(node.value, {
+    sourceType: 'module',
+    presets: ['env'],
+    plugins: ['jsx'],
+  });
+  if (ast.type === 'File' && ast.program.type === 'Program' && ast.program.body.length === 1) {
+    const exported = ast.program.body[0];
+    if (
+      exported.type === 'ExportNamedDeclaration' &&
+      exported.declaration.type === 'VariableDeclaration' &&
+      exported.declaration.declarations.length === 1
+    ) {
+      const declaration = exported.declaration.declarations[0];
+      if (declaration.type === 'VariableDeclarator' && declaration.id.type === 'Identifier') {
+        const { name } = declaration.id;
+        namedExports[name] = declaration.init;
+      }
+    }
+  }
+  return namedExports;
+};
+
+function extractExports(root, options) {
+  const namedExports = {};
+  root.children.forEach((child) => {
     if (child.type === 'jsx') {
       try {
         const ast = parser.parseExpression(child.value, { plugins: ['jsx'] });
@@ -320,16 +388,7 @@ function extractExports(node, options) {
             },
             value: {
               type: 'StringLiteral',
-              value: encodeURI(
-                ast.children
-                  .map(
-                    (el) =>
-                      generate(el, {
-                        quotes: 'double',
-                      }).code
-                  )
-                  .join('\n')
-              ),
+              value: getMdxSource(ast.children),
             },
           });
         }
@@ -350,6 +409,8 @@ function extractExports(node, options) {
          *
          */
       }
+    } else if (child.type === 'export') {
+      Object.assign(namedExports, getNamedExports(child));
     }
   });
   // we're overriding default export
@@ -359,8 +420,10 @@ function extractExports(node, options) {
   const context = {
     counter: 0,
     storyNameToKey: {},
+    root,
+    namedExports,
   };
-  node.children.forEach((n) => {
+  root.children.forEach((n) => {
     const exports = getExports(n, context, options);
     if (exports) {
       const { stories, meta } = exports;
@@ -389,7 +452,7 @@ function extractExports(node, options) {
   }
   metaExport.includeStories = JSON.stringify(includeStories);
 
-  const defaultJsx = mdxToJsx.toJSX(node, {}, { ...options, skipExport: true });
+  const defaultJsx = mdxToJsx.toJSX(root, {}, { ...options, skipExport: true });
   const fullJsx = [
     'import { assertIsFn, AddContext } from "@storybook/addon-docs/blocks";',
     defaultJsx,
@@ -405,7 +468,7 @@ function extractExports(node, options) {
 
 function createCompiler(mdxOptions) {
   return function compiler(options = {}) {
-    this.Compiler = (tree) => extractExports(tree, options, mdxOptions);
+    this.Compiler = (root) => extractExports(root, options, mdxOptions);
   };
 }