diff --git a/src/transformers/CJSImportTransformer.ts b/src/transformers/CJSImportTransformer.ts
index 98dce73c..4b0c115f 100644
--- a/src/transformers/CJSImportTransformer.ts
+++ b/src/transformers/CJSImportTransformer.ts
@@ -314,13 +314,81 @@ export default class CJSImportTransformer extends Transformer {
   }
 
   /**
-   * Transforms normal declaration exports, including handling destructuring.
+   * Transform a declaration like `export var`, `export let`, or `export const`.
+   */
+  private processExportVar(): void {
+    if (this.isSimpleExportVar()) {
+      this.processSimpleExportVar();
+    } else {
+      this.processComplexExportVar();
+    }
+  }
+
+  /**
+   * Determine if the export is of the form:
+   * export var/let/const [varName] = [expr];
+   * In other words, determine if function name inference might apply.
+   */
+  private isSimpleExportVar(): boolean {
+    let tokenIndex = this.tokens.currentIndex();
+    // export
+    tokenIndex++;
+    // var/let/const
+    tokenIndex++;
+    if (!this.tokens.matchesAtIndex(tokenIndex, [tt.name])) {
+      return false;
+    }
+    tokenIndex++;
+    while (tokenIndex < this.tokens.tokens.length && this.tokens.tokens[tokenIndex].isType) {
+      tokenIndex++;
+    }
+    if (!this.tokens.matchesAtIndex(tokenIndex, [tt.eq])) {
+      return false;
+    }
+    return true;
+  }
+
+  /**
+   * Transform an `export var` declaration initializing a single variable.
+   *
+   * For example, this:
+   * export const f = () => {};
+   * becomes this:
+   * const f = () => {}; exports.f = f;
+   *
+   * The variable is unused (e.g. exports.f has the true value of the export).
+   * We need to produce an assignment of this form so that the function will
+   * have an inferred name of "f", which wouldn't happen in the more general
+   * case below.
+   */
+  private processSimpleExportVar(): void {
+    // export
+    this.tokens.removeInitialToken();
+    // var/let/const
+    this.tokens.copyToken();
+    const varName = this.tokens.identifierName();
+    // x: number  ->  x
+    while (!this.tokens.matches1(tt.eq)) {
+      this.rootTransformer.processToken();
+    }
+    const endIndex = this.tokens.currentToken().rhsEndIndex;
+    if (endIndex == null) {
+      throw new Error("Expected = token with an end index.");
+    }
+    while (this.tokens.currentIndex() < endIndex) {
+      this.rootTransformer.processToken();
+    }
+    this.tokens.appendCode(`; exports.${varName} = ${varName}`);
+  }
+
+  /**
+   * Transform normal declaration exports, including handling destructuring.
    * For example, this:
    * export const {x: [a = 2, b], c} = d;
    * becomes this:
    * ({x: [exports.a = 2, exports.b], c: exports.c} = d;)
    */
-  private processExportVar(): void {
+  private processComplexExportVar(): void {
     this.tokens.removeInitialToken();
     this.tokens.removeToken();
     const needsParens = this.tokens.matches1(tt.braceL);
diff --git a/test/imports-test.ts b/test/imports-test.ts
index 0643068d..a023b324 100644
--- a/test/imports-test.ts
+++ b/test/imports-test.ts
@@ -78,9 +78,9 @@ describe("transform imports", () => {
       export const z = 3;
     `,
       `"use strict";${ESMODULE_PREFIX}
-       exports.x = 1;
-       exports.y = 2;
-       exports.z = 3;
+       var x = 1; exports.x = x;
+       let y = 2; exports.y = y;
+       const z = 3; exports.z = z;
     `,
     );
   });
@@ -623,7 +623,7 @@ module.exports = exports.default;
       export default 4;
     `,
       `"use strict";${ESMODULE_PREFIX}
-       exports.x = 1;
+       const x = 1; exports.x = x;
       exports. default = 4;
     `,
       {transforms: ["imports"], enableLegacyBabel5ModuleInterop: true},
@@ -981,7 +981,7 @@ module.exports = exports.default;
       console.log(a);
     `,
       `"use strict";${ESMODULE_PREFIX}
-       exports.a = 1;
+       let a = 1; exports.a = a;
       ({a: exports.a} = 2);
       exports.a = 3;
       console.log(exports.a);
@@ -1029,4 +1029,18 @@ module.exports = exports.default;
       {transforms: ["imports", "typescript"]},
     );
   });
+
+  it("allows function name inference for direct named exports", () => {
+    assertResult(
+      `
+      export let f = () => {};
+      export const g = () => {};
+    `,
+      `"use strict";${ESMODULE_PREFIX}
+       let f = () => {}; exports.f = f;
+       const g = () => {}; exports.g = g;
+    `,
+      {transforms: ["imports", "typescript"]},
+    );
+  });
 });
diff --git a/test/sucrase-test.ts b/test/sucrase-test.ts
index bdf65b1e..25062e6f 100644
--- a/test/sucrase-test.ts
+++ b/test/sucrase-test.ts
@@ -49,7 +49,7 @@ describe("sucrase", () => {
       };
     `,
       `"use strict";${ESMODULE_PREFIX}
-       exports.keywords = {
+       const keywords = {
         break: new KeywordTokenType("break"),
         case: new KeywordTokenType("case", { beforeExpr }),
         catch: new KeywordTokenType("catch"),
@@ -87,7 +87,7 @@ describe("sucrase", () => {
         typeof: new KeywordTokenType("typeof", { beforeExpr, prefix, startsExpr }),
         void: new KeywordTokenType("void", { beforeExpr, prefix, startsExpr }),
         delete: new KeywordTokenType("delete", { beforeExpr, prefix, startsExpr }),
-      };
+      }; exports.keywords = keywords;
     `,
     );
   });
diff --git a/test/types-test.ts b/test/types-test.ts
index dfac2cb7..22624ee5 100644
--- a/test/types-test.ts
+++ b/test/types-test.ts
@@ -208,7 +208,7 @@ describe("type transforms", () => {
     `,
       `"use strict";${ESMODULE_PREFIX}
       
-       exports.x = 1;
+       const x = 1; exports.x = x;
     `,
     );
   });