diff --git a/src/Psalm/Internal/Analyzer/FunctionLikeAnalyzer.php b/src/Psalm/Internal/Analyzer/FunctionLikeAnalyzer.php
index 61e03b550..47836c765 100644
--- a/src/Psalm/Internal/Analyzer/FunctionLikeAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/FunctionLikeAnalyzer.php
@@ -978,18 +978,6 @@ abstract class FunctionLikeAnalyzer extends SourceAnalyzer
                         $check_stmts = false;
                     }
                 }
-
-                if (!$storage instanceof MethodStorage
-                    && $param_type->hasTemplate()
-                    && $param_type->isSingle()
-                ) {
-                    /** @var Type\Atomic\TTemplateParam */
-                    $template_type = \array_values($param_type->getAtomicTypes())[0];
-
-                    if ($template_type->as->getTemplateTypes()) {
-                        $param_type = $template_type->as;
-                    }
-                }
             } else {
                 $param_type = Type::getMixed();
             }
diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/FunctionCallAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/FunctionCallAnalyzer.php
index 805a80d76..263cb8876 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/FunctionCallAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/FunctionCallAnalyzer.php
@@ -554,7 +554,16 @@ class FunctionCallAnalyzer extends CallAnalyzer
             $invalid_function_call_types = [];
             $has_valid_function_call_type = false;
 
-            foreach ($stmt_name_type->getAtomicTypes() as $var_type_part) {
+            $var_atomic_types = $stmt_name_type->getAtomicTypes();
+
+            while ($var_atomic_types) {
+                $var_type_part = \array_shift($var_atomic_types);
+
+                if ($var_type_part instanceof TTemplateParam) {
+                    $var_atomic_types = \array_merge($var_atomic_types, $var_type_part->as->getAtomicTypes());
+                    continue;
+                }
+
                 if ($var_type_part instanceof Type\Atomic\TClosure || $var_type_part instanceof TCallable) {
                     if (!$var_type_part->is_pure && $context->pure) {
                         if (IssueBuffer::accepts(
@@ -593,8 +602,6 @@ class FunctionCallAnalyzer extends CallAnalyzer
 
                     $function_call_info->function_exists = true;
                     $has_valid_function_call_type = true;
-                } elseif ($var_type_part instanceof TTemplateParam && $var_type_part->as->hasCallableType()) {
-                    $has_valid_function_call_type = true;
                 } elseif ($var_type_part instanceof TMixed || $var_type_part instanceof TTemplateParam) {
                     $has_valid_function_call_type = true;
 
diff --git a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/NewAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/NewAnalyzer.php
index de3dd1a97..2e85c59fc 100644
--- a/src/Psalm/Internal/Analyzer/Statements/Expression/Call/NewAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/Expression/Call/NewAnalyzer.php
@@ -569,7 +569,16 @@ class NewAnalyzer extends \Psalm\Internal\Analyzer\Statements\Expression\CallAna
 
         $new_type = null;
 
-        foreach ($stmt_class_type->getAtomicTypes() as $lhs_type_part) {
+        $stmt_class_types = $stmt_class_type->getAtomicTypes();
+
+        while ($stmt_class_types) {
+            $lhs_type_part = \array_shift($stmt_class_types);
+
+            if ($lhs_type_part instanceof Type\Atomic\TTemplateParam) {
+                $stmt_class_types = \array_merge($stmt_class_types, $lhs_type_part->as->getAtomicTypes());
+                continue;
+            }
+
             if ($lhs_type_part instanceof Type\Atomic\TTemplateParamClass) {
                 if (!$statements_analyzer->node_data->getType($stmt)) {
                     $new_type_part = new Type\Atomic\TTemplateParam(
@@ -735,9 +744,7 @@ class NewAnalyzer extends \Psalm\Internal\Analyzer\Statements\Expression\CallAna
                 )) {
                     // fall through
                 }
-            } elseif ($lhs_type_part instanceof Type\Atomic\TMixed
-                || $lhs_type_part instanceof Type\Atomic\TTemplateParam
-            ) {
+            } elseif ($lhs_type_part instanceof Type\Atomic\TMixed) {
                 if (IssueBuffer::accepts(
                     new MixedMethodCall(
                         'Cannot call constructor on an unknown class',
diff --git a/src/Psalm/Internal/Type/SimpleAssertionReconciler.php b/src/Psalm/Internal/Type/SimpleAssertionReconciler.php
index 7db56ceae..c012dad30 100644
--- a/src/Psalm/Internal/Type/SimpleAssertionReconciler.php
+++ b/src/Psalm/Internal/Type/SimpleAssertionReconciler.php
@@ -1995,12 +1995,24 @@ class SimpleAssertionReconciler extends \Psalm\Type\Reconciler
                 $callable_types[] = $type;
                 $did_remove_type = true;
             } elseif ($type instanceof TTemplateParam) {
-                if ($type->as->isMixed()) {
+                if ($type->as->hasCallableType() || $type->as->hasMixed()) {
                     $type = clone $type;
-                    $type->as = new Type\Union([new Type\Atomic\TCallable]);
+
+                    $type->as = self::reconcileCallable(
+                        $codebase,
+                        $type->as,
+                        null,
+                        $negated,
+                        null,
+                        $suppressed_issues,
+                        $failed_reconciliation,
+                        $is_equality
+                    );
                 }
-                $callable_types[] = $type;
+
                 $did_remove_type = true;
+
+                $callable_types[] = $type;
             } else {
                 $did_remove_type = true;
             }
diff --git a/tests/Template/ConditionalReturnTypeTest.php b/tests/Template/ConditionalReturnTypeTest.php
index 98f451a59..ef07b4f83 100644
--- a/tests/Template/ConditionalReturnTypeTest.php
+++ b/tests/Template/ConditionalReturnTypeTest.php
@@ -711,6 +711,40 @@ class ConditionalReturnTypeTest extends TestCase
                         return new NullObject();
                     }'
             ],
+            'reconcileCallableFunctionTemplateParam' => [
+                '<?php
+                    /**
+                     * @template T
+                     * @template TOptionalClosure as (callable():T)|null
+                     * @param TOptionalClosure $cb
+                     * @return (TOptionalClosure is null ? int : T)
+                     */
+                    function f($cb) {
+                        if (is_callable($cb)) {
+                            return $cb();
+                        }
+
+                        return 1;
+                    }'
+            ],
+            'reconcileCallableClassTemplateParam' => [
+                '<?php
+                    class C {
+                        /**
+                         * @template T
+                         * @template TOptionalClosure as (callable():T)|null
+                         * @param TOptionalClosure $cb
+                         * @return (TOptionalClosure is null ? int : T)
+                         */
+                        public static function f($cb) {
+                            if (is_callable($cb)) {
+                                return $cb();
+                            }
+
+                            return 1;
+                        }
+                    }'
+            ],
         ];
     }
 }