diff --git a/src/rules/noUnsafeAnyRule.ts b/src/rules/noUnsafeAnyRule.ts
index d5cfc992c7a..7e8ea790a34 100644
--- a/src/rules/noUnsafeAnyRule.ts
+++ b/src/rules/noUnsafeAnyRule.ts
@@ -47,14 +47,13 @@ export class Rule extends Lint.Rules.TypedRule {
 const isExpression: (node: ts.Node) => node is ts.Expression = (ts as any).isExpression;
 
 function walk(ctx: Lint.WalkContext<void>, checker: ts.TypeChecker): void {
-    return ts.forEachChild(ctx.sourceFile, recur);
-    function recur(node: ts.Node): void {
+    return ts.forEachChild(ctx.sourceFile, function cb(node: ts.Node): void {
         if (isExpression(node) && isAny(checker.getTypeAtLocation(node)) && !isAllowedLocation(node, checker)) {
             ctx.addFailureAtNode(node, Rule.FAILURE_STRING);
         } else {
-            return ts.forEachChild(node, recur);
+            return ts.forEachChild(node, cb);
         }
-    }
+    });
 }
 
 function isAllowedLocation(node: ts.Expression, { getContextualType, getTypeAtLocation }: ts.TypeChecker): boolean {
@@ -67,6 +66,13 @@ function isAllowedLocation(node: ts.Expression, { getContextualType, getTypeAtLo
         // Allow casts
         case ts.SyntaxKind.TypeAssertionExpression:
         case ts.SyntaxKind.AsExpression:
+        // Allow imports
+        case ts.SyntaxKind.ImportEqualsDeclaration:
+        case ts.SyntaxKind.ExternalModuleReference:
+        case ts.SyntaxKind.ImportDeclaration:
+        case ts.SyntaxKind.NamespaceImport:
+        case ts.SyntaxKind.ImportSpecifier:
+        case ts.SyntaxKind.ImportClause:
             return true;
 
         // OK to pass 'any' to a function that takes 'any' as its argument
@@ -91,10 +97,12 @@ function isAllowedLocation(node: ts.Expression, { getContextualType, getTypeAtLo
                     return false;
             }
 
-        // Allow `const x = foo;`, but not `const x: Foo = foo;`.
-        case ts.SyntaxKind.VariableDeclaration:
-            return Lint.hasModifier(parent.parent!.parent!.modifiers, ts.SyntaxKind.DeclareKeyword) ||
-                (parent as ts.VariableDeclaration).type === undefined;
+        // Allow `const x = foo;` and `const x: any = foo`, but not `const x: Foo = foo;`.
+        case ts.SyntaxKind.VariableDeclaration: {
+            const { name, type } = parent as ts.VariableDeclaration;
+            // Always allow the LHS to be `any`. Just don't allow RHS to be `any` when LHS isn't.
+            return node === name || type === undefined || type.kind === ts.SyntaxKind.AnyKeyword;
+        }
 
         case ts.SyntaxKind.PropertyAccessExpression:
             // Don't warn for right hand side; this is redundant if we warn for the left-hand side.
diff --git a/test/rules/no-unsafe-any/commonjsModule.ts b/test/rules/no-unsafe-any/commonjsModule.ts
new file mode 100644
index 00000000000..d38fad21b9c
--- /dev/null
+++ b/test/rules/no-unsafe-any/commonjsModule.ts
@@ -0,0 +1,3 @@
+const x: any = 0;
+namespace x {}
+export = x;
diff --git a/test/rules/no-unsafe-any/es6Module.ts b/test/rules/no-unsafe-any/es6Module.ts
new file mode 100644
index 00000000000..592305a9d7e
--- /dev/null
+++ b/test/rules/no-unsafe-any/es6Module.ts
@@ -0,0 +1,3 @@
+const defaultExport: any = 0;
+export default defaultExport;
+export const namedExport: any = 0;
diff --git a/test/rules/no-unsafe-any/test.ts.lint b/test/rules/no-unsafe-any/test.ts.lint
index 7222f2ddb10..142a3d8dcf4 100644
--- a/test/rules/no-unsafe-any/test.ts.lint
+++ b/test/rules/no-unsafe-any/test.ts.lint
@@ -1,3 +1,10 @@
+import importEquals = require("./commonjsModule");
+import importAlias = modA;
+namespace N { const x: any = 0; }
+import importQualifiedName = N.x;
+import * as namespaceImport from "./commonjsModule";
+import defaultExport, { namedExport } from "./es6Module";
+
 declare const x: any;
 
 function f(x: any) {