diff --git a/src/Psalm/Checker/Statements/Expression/Call/FunctionCallChecker.php b/src/Psalm/Checker/Statements/Expression/Call/FunctionCallChecker.php
index 50d67da8c..7b34c4f90 100644
--- a/src/Psalm/Checker/Statements/Expression/Call/FunctionCallChecker.php
+++ b/src/Psalm/Checker/Statements/Expression/Call/FunctionCallChecker.php
@@ -40,41 +40,41 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
         PhpParser\Node\Expr\FuncCall $stmt,
         Context $context
     ) {
-        $method = $stmt->name;
+        $function = $stmt->name;
 
-        if ($method instanceof PhpParser\Node\Name) {
+        if ($function instanceof PhpParser\Node\Name) {
             $first_arg = isset($stmt->args[0]) ? $stmt->args[0] : null;
 
-            if ($method->parts === ['method_exists']) {
+            if ($function->parts === ['method_exists']) {
                 $context->check_methods = false;
-            } elseif ($method->parts === ['class_exists']) {
+            } elseif ($function->parts === ['class_exists']) {
                 if ($first_arg && $first_arg->value instanceof PhpParser\Node\Scalar\String_) {
                     $context->addPhantomClass($first_arg->value->value);
                 } else {
                     $context->check_classes = false;
                 }
-            } elseif ($method->parts === ['extension_loaded']) {
+            } elseif ($function->parts === ['extension_loaded']) {
                 $context->check_classes = false;
-            } elseif ($method->parts === ['function_exists']) {
+            } elseif ($function->parts === ['function_exists']) {
                 $context->check_functions = false;
-            } elseif ($method->parts === ['is_callable']) {
+            } elseif ($function->parts === ['is_callable']) {
                 $context->check_methods = false;
                 $context->check_functions = false;
-            } elseif ($method->parts === ['defined']) {
+            } elseif ($function->parts === ['defined']) {
                 $context->check_consts = false;
-            } elseif ($method->parts === ['extract']) {
+            } elseif ($function->parts === ['extract']) {
                 $context->check_variables = false;
-            } elseif ($method->parts === ['var_dump'] || $method->parts === ['shell_exec']) {
+            } elseif ($function->parts === ['var_dump'] || $function->parts === ['shell_exec']) {
                 if (IssueBuffer::accepts(
                     new ForbiddenCode(
-                        'Unsafe ' . implode('', $method->parts),
+                        'Unsafe ' . implode('', $function->parts),
                         new CodeLocation($statements_checker->getSource(), $stmt)
                     ),
                     $statements_checker->getSuppressedIssues()
                 )) {
                     return false;
                 }
-            } elseif ($method->parts === ['define']) {
+            } elseif ($function->parts === ['define']) {
                 if ($first_arg && $first_arg->value instanceof PhpParser\Node\Scalar\String_) {
                     $second_arg = $stmt->args[1];
                     ExpressionChecker::analyze($statements_checker, $second_arg->value, $context);
@@ -91,7 +91,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
             }
         }
 
-        $method_id = null;
+        $function_id = null;
         $function_params = null;
         $in_call_map = false;
 
@@ -209,21 +209,21 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 $stmt->inferredType = Type::getMixed();
             }
         } else {
-            $method_id = implode('\\', $stmt->name->parts);
+            $function_id = implode('\\', $stmt->name->parts);
 
-            $in_call_map = CallMap::inCallMap($method_id);
-            $is_stubbed = $codebase_functions->hasStubbedFunction($method_id);
+            $in_call_map = CallMap::inCallMap($function_id);
+            $is_stubbed = $codebase_functions->hasStubbedFunction($function_id);
 
             $is_predefined = true;
 
             if (!$in_call_map) {
                 $predefined_functions = $config->getPredefinedFunctions();
-                $is_predefined = isset($predefined_functions[$method_id]);
+                $is_predefined = isset($predefined_functions[$function_id]);
             }
 
             if (!$in_call_map && !$stmt->name instanceof PhpParser\Node\Name\FullyQualified) {
-                $method_id = $codebase_functions->getFullyQualifiedFunctionNameFromString(
-                    $method_id,
+                $function_id = $codebase_functions->getFullyQualifiedFunctionNameFromString(
+                    $function_id,
                     $statements_checker
                 );
             }
@@ -232,17 +232,19 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 if ($context->check_functions) {
                     if (self::checkFunctionExists(
                         $statements_checker,
-                        $method_id,
+                        $function_id,
                         $code_location
                     ) === false
                     ) {
                         return false;
                     }
+                } else {
+                    $function_id = self::getExistingFunctionId($statements_checker, $function_id);
                 }
 
                 $function_exists = $is_stubbed || $codebase_functions->functionExists(
                     $statements_checker,
-                    strtolower($method_id)
+                    strtolower($function_id)
                 );
             } else {
                 $function_exists = true;
@@ -252,7 +254,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 if (!$in_call_map || $is_stubbed) {
                     $function_storage = $codebase_functions->getStorage(
                         $statements_checker,
-                        strtolower($method_id)
+                        strtolower($function_id)
                     );
 
                     $function_params = $function_storage->params;
@@ -265,7 +267,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 if ($in_call_map && !$is_stubbed) {
                     $function_params = FunctionLikeChecker::getFunctionParamsFromCallMapById(
                         $statements_checker->getFileChecker()->project_checker,
-                        $method_id,
+                        $function_id,
                         $stmt->args
                     );
                 }
@@ -276,7 +278,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
             $statements_checker,
             $stmt->args,
             $function_params,
-            $method_id,
+            $function_id,
             $context
         ) === false) {
             // fall through
@@ -285,11 +287,11 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
         if ($function_exists) {
             $generic_params = null;
 
-            if ($stmt->name instanceof PhpParser\Node\Name && $method_id) {
+            if ($stmt->name instanceof PhpParser\Node\Name && $function_id) {
                 if (!$is_stubbed && $in_call_map) {
                     $function_params = FunctionLikeChecker::getFunctionParamsFromCallMapById(
                         $statements_checker->getFileChecker()->project_checker,
-                        $method_id,
+                        $function_id,
                         $stmt->args
                     );
                 }
@@ -299,7 +301,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
             if (self::checkFunctionLikeArgumentsMatch(
                 $statements_checker,
                 $stmt->args,
-                $method_id,
+                $function_id,
                 $function_params ?: [],
                 $function_storage,
                 null,
@@ -310,7 +312,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 // fall through
             }
 
-            if ($stmt->name instanceof PhpParser\Node\Name && $method_id) {
+            if ($stmt->name instanceof PhpParser\Node\Name && $function_id) {
                 if (!$in_call_map || $is_stubbed) {
                     if ($function_storage && $function_storage->template_types) {
                         foreach ($function_storage->template_types as $template_name => $_) {
@@ -355,7 +357,7 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
                 } else {
                     $stmt->inferredType = FunctionChecker::getReturnTypeFromCallMapWithArgs(
                         $statements_checker,
-                        $method_id,
+                        $function_id,
                         $stmt->args,
                         $code_location,
                         $statements_checker->getSuppressedIssues()
@@ -369,8 +371,8 @@ class FunctionCallChecker extends \Psalm\Checker\Statements\Expression\CallCheck
             }
 
             if ($config->use_assert_for_type &&
-                $method instanceof PhpParser\Node\Name &&
-                $method->parts === ['assert'] &&
+                $function instanceof PhpParser\Node\Name &&
+                $function->parts === ['assert'] &&
                 isset($stmt->args[0])
             ) {
                 $assert_clauses = AlgebraChecker::getFormula(
diff --git a/src/Psalm/Checker/Statements/Expression/CallChecker.php b/src/Psalm/Checker/Statements/Expression/CallChecker.php
index 08a71a60b..67a422a77 100644
--- a/src/Psalm/Checker/Statements/Expression/CallChecker.php
+++ b/src/Psalm/Checker/Statements/Expression/CallChecker.php
@@ -1414,4 +1414,31 @@ class CallChecker
 
         return true;
     }
+
+    /**
+     * @param  StatementsChecker    $statements_checker
+     * @param  string               $function_id
+     *
+     * @return string
+     */
+    protected static function getExistingFunctionId(StatementsChecker $statements_checker, $function_id)
+    {
+        $function_id = strtolower($function_id);
+
+        $codebase = $statements_checker->getFileChecker()->project_checker->codebase;
+
+        if ($codebase->functions->functionExists($statements_checker, $function_id)) {
+            return $function_id;
+        }
+
+        $root_function_id = preg_replace('/.*\\\/', '', $function_id);
+
+        if ($function_id !== $root_function_id
+            && $codebase->functions->functionExists($statements_checker, $root_function_id)
+        ) {
+            return $root_function_id;
+        }
+
+        return $function_id;
+    }
 }
diff --git a/src/Psalm/Codebase/Functions.php b/src/Psalm/Codebase/Functions.php
index 7b83d3c46..cccecdd77 100644
--- a/src/Psalm/Codebase/Functions.php
+++ b/src/Psalm/Codebase/Functions.php
@@ -39,8 +39,8 @@ class Functions
      */
     public function getStorage(StatementsChecker $statements_checker, $function_id)
     {
-        if (isset(self::$stubbed_functions[$function_id])) {
-            return self::$stubbed_functions[$function_id];
+        if (isset(self::$stubbed_functions[strtolower($function_id)])) {
+            return self::$stubbed_functions[strtolower($function_id)];
         }
 
         if ($this->reflection->hasFunction($function_id)) {
@@ -96,7 +96,7 @@ class Functions
      */
     public function addStubbedFunction($function_id, FunctionLikeStorage $storage)
     {
-        self::$stubbed_functions[$function_id] = $storage;
+        self::$stubbed_functions[strtolower($function_id)] = $storage;
     }
 
     /**
@@ -106,7 +106,7 @@ class Functions
      */
     public function hasStubbedFunction($function_id)
     {
-        return isset(self::$stubbed_functions[$function_id]);
+        return isset(self::$stubbed_functions[strtolower($function_id)]);
     }
 
     /**
@@ -126,7 +126,7 @@ class Functions
             return true;
         }
 
-        if (isset(self::$stubbed_functions[$function_id])) {
+        if (isset(self::$stubbed_functions[strtolower($function_id)])) {
             return true;
         }
 
diff --git a/tests/ConfigTest.php b/tests/ConfigTest.php
index 0d56fe90c..734976cfe 100644
--- a/tests/ConfigTest.php
+++ b/tests/ConfigTest.php
@@ -395,6 +395,73 @@ class ConfigTest extends TestCase
         $this->analyzeFile($file_path, new Context());
     }
 
+    /**
+     * @return void
+     */
+    public function testStubFunctionWithFunctionExists()
+    {
+        $this->project_checker = $this->getProjectCheckerWithConfig(
+            TestConfig::loadFromXML(
+                dirname(__DIR__),
+                '<?xml version="1.0"?>
+                <psalm>
+                    <projectFiles>
+                        <directory name="src" />
+                    </projectFiles>
+
+                    <stubs>
+                        <file name="tests/stubs/custom_functions.php" />
+                    </stubs>
+                </psalm>'
+            )
+        );
+
+        $file_path = getcwd() . '/src/somefile.php';
+
+        $this->addFile(
+            $file_path,
+            '<?php
+                function_exists("fooBar");
+                echo barBar("hello");'
+        );
+
+        $this->analyzeFile($file_path, new Context());
+    }
+
+    /**
+     * @return void
+     */
+    public function testNamespacedStubFunctionWithFunctionExists()
+    {
+        $this->project_checker = $this->getProjectCheckerWithConfig(
+            TestConfig::loadFromXML(
+                dirname(__DIR__),
+                '<?xml version="1.0"?>
+                <psalm>
+                    <projectFiles>
+                        <directory name="src" />
+                    </projectFiles>
+
+                    <stubs>
+                        <file name="tests/stubs/custom_functions.php" />
+                    </stubs>
+                </psalm>'
+            )
+        );
+
+        $file_path = getcwd() . '/src/somefile.php';
+
+        $this->addFile(
+            $file_path,
+            '<?php
+                namespace A;
+                function_exists("fooBar");
+                echo barBar("hello");'
+        );
+
+        $this->analyzeFile($file_path, new Context());
+    }
+
     /**
      * @expectedException        \Psalm\Exception\CodeException
      * @expectedExceptionMessage UndefinedFunction - /src/somefile.php:2 - Function barBar does not exist