diff --git a/src/Analyser/NodeScopeResolver.php b/src/Analyser/NodeScopeResolver.php
index cbed5105ae..abd0066be9 100644
--- a/src/Analyser/NodeScopeResolver.php
+++ b/src/Analyser/NodeScopeResolver.php
@@ -3917,7 +3917,7 @@ private function tryProcessUnrolledConstantArrayForeach(
 		$matchedNativeArrays = count($nativeConstantArrays) === count($constantArrays) ? $nativeConstantArrays : null;
 
 		$valueVarName = $stmt->valueVar->name;
-		$keyVarName = $stmt->keyVar instanceof Variable && is_string($stmt->keyVar->name) ? $stmt->keyVar->name : null;
+		$keyVarName = $stmt->keyVar instanceof Variable ? $stmt->keyVar->name : null;
 
 		$allBodyScopes = [];
 		$allChainScopes = [];
@@ -4052,7 +4052,7 @@ private function enterForeach(MutatingScope $scope, ExpressionResultStorage $sto
 			&& ($stmt->keyVar === null || ($stmt->keyVar instanceof Variable && is_string($stmt->keyVar->name)))
 		) {
 			$keyVarName = null;
-			if ($stmt->keyVar instanceof Variable && is_string($stmt->keyVar->name)) {
+			if ($stmt->keyVar instanceof Variable) {
 				$keyVarName = $stmt->keyVar->name;
 			}
 			$scope = $scope->enterForeach(
diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index 9f7a86eb4a..0649379fdf 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -596,7 +596,7 @@ public function specifyTypesInCondition(
 			}
 
 			return $this->handleDefaultTruthyOrFalseyContext($context, $expr, $scope);
-		} elseif ($expr instanceof FuncCall && !($expr->name instanceof Name)) {
+		} elseif ($expr instanceof FuncCall) {
 			$specifiedTypes = $this->specifyTypesFromCallableCall($context, $expr, $scope);
 			if ($specifiedTypes !== null) {
 				return $specifiedTypes;
@@ -754,10 +754,10 @@ public function specifyTypesInCondition(
 					$result = $result->setAlwaysOverwriteTypes();
 				}
 				return $result->setNewConditionalExpressionHolders(array_merge(
-					$this->processBooleanNotSureConditionalTypes($scope, $leftTypesForHolders, $rightTypesForHolders),
-					$this->processBooleanNotSureConditionalTypes($scope, $rightTypesForHolders, $leftTypesForHolders),
-					$this->processBooleanSureConditionalTypes($scope, $leftTypesForHolders, $rightTypesForHolders),
-					$this->processBooleanSureConditionalTypes($scope, $rightTypesForHolders, $leftTypesForHolders),
+					$this->processBooleanNotSureConditionalTypes($scope, $leftTypesForHolders, $rightTypesForHolders, $rightScope),
+					$this->processBooleanNotSureConditionalTypes($scope, $rightTypesForHolders, $leftTypesForHolders, $scope),
+					$this->processBooleanSureConditionalTypes($scope, $leftTypesForHolders, $rightTypesForHolders, $rightScope),
+					$this->processBooleanSureConditionalTypes($scope, $rightTypesForHolders, $leftTypesForHolders, $scope),
 				))->setRootExpr($expr);
 			}
 
@@ -804,10 +804,10 @@ public function specifyTypesInCondition(
 					$result = $result->setAlwaysOverwriteTypes();
 				}
 				return $result->setNewConditionalExpressionHolders(array_merge(
-					$this->processBooleanNotSureConditionalTypes($scope, $leftTypes, $rightTypes),
-					$this->processBooleanNotSureConditionalTypes($scope, $rightTypes, $leftTypes),
-					$this->processBooleanSureConditionalTypes($scope, $leftTypes, $rightTypes),
-					$this->processBooleanSureConditionalTypes($scope, $rightTypes, $leftTypes),
+					$this->processBooleanNotSureConditionalTypes($scope, $leftTypes, $rightTypes, $rightScope),
+					$this->processBooleanNotSureConditionalTypes($scope, $rightTypes, $leftTypes, $scope),
+					$this->processBooleanSureConditionalTypes($scope, $leftTypes, $rightTypes, $rightScope),
+					$this->processBooleanSureConditionalTypes($scope, $rightTypes, $leftTypes, $scope),
 				))->setRootExpr($expr);
 			}
 
@@ -2079,14 +2079,11 @@ private function augmentBooleanOrTruthyWithConditionalHolders(MutatingScope $sco
 	/**
 	 * @return array<string, ConditionalExpressionHolder[]>
 	 */
-	private function processBooleanSureConditionalTypes(Scope $scope, SpecifiedTypes $leftTypes, SpecifiedTypes $rightTypes): array
+	private function processBooleanSureConditionalTypes(Scope $scope, SpecifiedTypes $leftTypes, SpecifiedTypes $rightTypes, Scope $rightScope): array
 	{
 		$conditionExpressionTypes = [];
 		foreach ($leftTypes->getSureTypes() as $exprString => [$expr, $type]) {
-			if (!$expr instanceof Expr\Variable) {
-				continue;
-			}
-			if (!is_string($expr->name)) {
+			if (!$this->isTrackableExpression($expr)) {
 				continue;
 			}
 
@@ -2105,10 +2102,7 @@ private function processBooleanSureConditionalTypes(Scope $scope, SpecifiedTypes
 		if (count($conditionExpressionTypes) > 0) {
 			$holders = [];
 			foreach ($rightTypes->getSureTypes() as $exprString => [$expr, $type]) {
-				if (!$expr instanceof Expr\Variable) {
-					continue;
-				}
-				if (!is_string($expr->name)) {
+				if (!$this->isTrackableExpression($expr)) {
 					continue;
 				}
 
@@ -2118,27 +2112,19 @@ private function processBooleanSureConditionalTypes(Scope $scope, SpecifiedTypes
 
 				$conditions = $conditionExpressionTypes;
 				foreach ($conditions as $conditionExprString => $conditionExprTypeHolder) {
-					$conditionExpr = $conditionExprTypeHolder->getExpr();
-					if (!$conditionExpr instanceof Expr\Variable) {
-						continue;
+					if ($conditionExprString === $exprString) {
+						unset($conditions[$conditionExprString]);
 					}
-					if (!is_string($conditionExpr->name)) {
-						continue;
-					}
-					if ($conditionExpr->name !== $expr->name) {
-						continue;
-					}
-
-					unset($conditions[$conditionExprString]);
 				}
 
 				if (count($conditions) === 0) {
 					continue;
 				}
 
+				$targetScope = $expr instanceof Expr\Variable ? $scope : $rightScope;
 				$holder = new ConditionalExpressionHolder(
 					$conditions,
-					ExpressionTypeHolder::createYes($expr, TypeCombinator::intersect($scope->getType($expr), $type)),
+					ExpressionTypeHolder::createYes($expr, TypeCombinator::intersect($targetScope->getType($expr), $type)),
 				);
 				$holders[$exprString][$holder->getKey()] = $holder;
 			}
@@ -2149,6 +2135,17 @@ private function processBooleanSureConditionalTypes(Scope $scope, SpecifiedTypes
 		return [];
 	}
 
+	private function isTrackableExpression(Expr $expr): bool
+	{
+		if ($expr instanceof Expr\Variable) {
+			return is_string($expr->name);
+		}
+
+		return $expr instanceof Expr\PropertyFetch
+			|| $expr instanceof Expr\ArrayDimFetch
+			|| $expr instanceof Expr\StaticPropertyFetch;
+	}
+
 	/**
 	 * Flatten a deep BooleanOr chain into leaf expressions and process them
 	 * without recursive filterByFalseyValue calls. This reduces O(n^2) to O(n)
@@ -2279,14 +2276,11 @@ private function specifyTypesForFlattenedBooleanAnd(
 	/**
 	 * @return array<string, ConditionalExpressionHolder[]>
 	 */
-	private function processBooleanNotSureConditionalTypes(Scope $scope, SpecifiedTypes $leftTypes, SpecifiedTypes $rightTypes): array
+	private function processBooleanNotSureConditionalTypes(Scope $scope, SpecifiedTypes $leftTypes, SpecifiedTypes $rightTypes, Scope $rightScope): array
 	{
 		$conditionExpressionTypes = [];
 		foreach ($leftTypes->getSureNotTypes() as $exprString => [$expr, $type]) {
-			if (!$expr instanceof Expr\Variable) {
-				continue;
-			}
-			if (!is_string($expr->name)) {
+			if (!$this->isTrackableExpression($expr)) {
 				continue;
 			}
 
@@ -2299,10 +2293,7 @@ private function processBooleanNotSureConditionalTypes(Scope $scope, SpecifiedTy
 		if (count($conditionExpressionTypes) > 0) {
 			$holders = [];
 			foreach ($rightTypes->getSureNotTypes() as $exprString => [$expr, $type]) {
-				if (!$expr instanceof Expr\Variable) {
-					continue;
-				}
-				if (!is_string($expr->name)) {
+				if (!$this->isTrackableExpression($expr)) {
 					continue;
 				}
 
@@ -2312,27 +2303,19 @@ private function processBooleanNotSureConditionalTypes(Scope $scope, SpecifiedTy
 
 				$conditions = $conditionExpressionTypes;
 				foreach ($conditions as $conditionExprString => $conditionExprTypeHolder) {
-					$conditionExpr = $conditionExprTypeHolder->getExpr();
-					if (!$conditionExpr instanceof Expr\Variable) {
-						continue;
-					}
-					if (!is_string($conditionExpr->name)) {
-						continue;
+					if ($conditionExprString === $exprString) {
+						unset($conditions[$conditionExprString]);
 					}
-					if ($conditionExpr->name !== $expr->name) {
-						continue;
-					}
-
-					unset($conditions[$conditionExprString]);
 				}
 
 				if (count($conditions) === 0) {
 					continue;
 				}
 
+				$targetScope = $expr instanceof Expr\Variable ? $scope : $rightScope;
 				$holder = new ConditionalExpressionHolder(
 					$conditions,
-					ExpressionTypeHolder::createYes($expr, TypeCombinator::remove($scope->getType($expr), $type)),
+					ExpressionTypeHolder::createYes($expr, TypeCombinator::remove($targetScope->getType($expr), $type)),
 				);
 				$holders[$exprString][$holder->getKey()] = $holder;
 			}
@@ -2586,6 +2569,49 @@ private function createForExpr(
 			}
 		}
 
+		if (
+			$expr instanceof ArrayDimFetch
+			&& $expr->dim !== null
+			&& !$context->null()
+		) {
+			$dimType = $scope->getType($expr->dim)->toArrayKey();
+			if ($dimType instanceof ConstantIntegerType || $dimType->getConstantStrings() !== []) {
+				$varType = $scope->getType($expr->var);
+				$constantArrays = $varType->getConstantArrays();
+				if ($constantArrays !== []) {
+					$refinedArrays = [];
+					$changed = false;
+					foreach ($constantArrays as $constantArray) {
+						if (!$constantArray->hasOffsetValueType($dimType)->yes()) {
+							$refinedArrays[] = $constantArray;
+							continue;
+						}
+						$offsetValueType = $constantArray->getOffsetValueType($dimType);
+						if ($context->false()) {
+							$narrowedValueType = TypeCombinator::remove($offsetValueType, $type);
+						} else {
+							$narrowedValueType = TypeCombinator::intersect($offsetValueType, $type);
+						}
+						if ($narrowedValueType instanceof NeverType) {
+							$changed = true;
+							continue;
+						}
+						if (!$narrowedValueType->equals($offsetValueType)) {
+							$changed = true;
+							$refinedArrays[] = $constantArray->setExistingOffsetValueType($dimType, $narrowedValueType);
+						} else {
+							$refinedArrays[] = $constantArray;
+						}
+					}
+
+					if ($changed && $refinedArrays !== []) {
+						$varExprString = $this->exprPrinter->printExpr($expr->var);
+						$sureTypes[$varExprString] = [$expr->var, TypeCombinator::union(...$refinedArrays)];
+					}
+				}
+			}
+		}
+
 		$types = new SpecifiedTypes($sureTypes, $sureNotTypes);
 		if (isset($containsNull) && !$containsNull) {
 			return $this->createNullsafeTypes($originalExpr, $scope, $context, $type)->unionWith($types);
diff --git a/src/Type/Constant/ConstantArrayTypeBuilder.php b/src/Type/Constant/ConstantArrayTypeBuilder.php
index 894fbfc4f1..cd7f5aa026 100644
--- a/src/Type/Constant/ConstantArrayTypeBuilder.php
+++ b/src/Type/Constant/ConstantArrayTypeBuilder.php
@@ -120,10 +120,6 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $opt
 			}
 
 			if ($offsetType === null) {
-				if (count($this->nextAutoIndexes) === 0) {
-					return;
-				}
-
 				$newAutoIndexes = $optional ? $this->nextAutoIndexes : [];
 				$hasOptional = false;
 				foreach ($this->keyTypes as $i => $keyType) {
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14566.php b/tests/PHPStan/Analyser/nsrt/bug-14566.php
new file mode 100644
index 0000000000..ec6005247c
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14566.php
@@ -0,0 +1,133 @@
+<?php
+
+declare(strict_types = 1);
+
+namespace Bug14566;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param array{}|array{hi: 'hello'}|array{hi: array{0: 42, 1?: 42}} $test
+ */
+function foo(array $test): void {
+	if (isset($test['hi']) && is_string($test['hi'])) {
+		return;
+	}
+	assertType("array{}|array{hi: array{0: 42, 1?: 42}}", $test);
+	assertType("array{0: 42, 1?: 42}", $test['hi']);
+}
+
+/**
+ * @param array{}|array{hi: 'hello'}|array{hi: array{0: 42, 1?: 42}} $test
+ */
+function fooOr(array $test): void {
+	if (!isset($test['hi']) || !is_string($test['hi'])) {
+		assertType("array{}|array{hi: array{0: 42, 1?: 42}}", $test);
+		return;
+	}
+	assertType("array{hi: 'hello'}", $test);
+}
+
+/**
+ * @param array{}|array{hi: 42}|array{hi: 'hello'} $test
+ */
+function fooIsInt(array $test): void {
+	if (isset($test['hi']) && is_int($test['hi'])) {
+		return;
+	}
+	assertType("array{}|array{hi: 'hello'}", $test);
+}
+
+/**
+ * @param array{}|array{hi: 'hello'}|array{hi: array{0: 42}} $test
+ */
+function fooIsArray(array $test): void {
+	if (isset($test['hi']) && is_array($test['hi'])) {
+		return;
+	}
+	assertType("array{}|array{hi: 'hello'}", $test);
+}
+
+/**
+ * @param array{}|array{hi: \stdClass}|array{hi: 'hello'} $test
+ */
+function fooInstanceof(array $test): void {
+	if (isset($test['hi']) && $test['hi'] instanceof \stdClass) {
+		return;
+	}
+	assertType("array{}|array{hi: 'hello'}", $test);
+}
+
+/**
+ * @param array{}|array{hi: string|int}|array{hi: float} $test
+ */
+function fooPartialOverlap(array $test): void {
+	if (isset($test['hi']) && is_string($test['hi'])) {
+		return;
+	}
+	assertType("array{}|array{hi: float}|array{hi: int}", $test);
+}
+
+/**
+ * @param array{}|array{hi: string|int}|array{hi: float} $test
+ */
+function fooPartialOverlapOr(array $test): void {
+	if (!isset($test['hi']) || !is_string($test['hi'])) {
+		assertType("array{}|array{hi: float}|array{hi: int}", $test);
+		return;
+	}
+	assertType("array{hi: string}", $test);
+}
+
+/**
+ * Regression: conditional holders for property fetches must use the right-side
+ * scope (where the base object is narrowed) to precompute the target type.
+ * Otherwise, accessing $node->name when $node is CallLike (which has no $name
+ * property) produces ErrorType.
+ */
+function fooElseifPropertyNarrowing(\PhpParser\Node\Expr\CallLike $node, \PHPStan\Analyser\Scope $scope): void {
+	if ($node instanceof \PhpParser\Node\Expr\MethodCall && $node->name instanceof \PhpParser\Node\Identifier) {
+		assertType('PhpParser\Node\Expr\MethodCall', $node);
+		assertType('PhpParser\Node\Identifier', $node->name);
+	} elseif ($node instanceof \PhpParser\Node\Expr\StaticCall && $node->name instanceof \PhpParser\Node\Identifier && $node->class instanceof \PhpParser\Node\Name) {
+		assertType('PhpParser\Node\Expr\StaticCall', $node);
+		assertType('PhpParser\Node\Identifier', $node->name);
+		assertType('PhpParser\Node\Name', $node->class);
+	} elseif ($node instanceof \PhpParser\Node\Expr\New_ && $node->class instanceof \PhpParser\Node\Name) {
+		assertType('PhpParser\Node\Expr\New_', $node);
+		assertType('PhpParser\Node\Name', $node->class);
+	} elseif ($node instanceof \PhpParser\Node\Expr\FuncCall && $node->name instanceof \PhpParser\Node\Name) {
+		assertType('PhpParser\Node\Expr\FuncCall', $node);
+		assertType('PhpParser\Node\Name', $node->name);
+	} elseif ($node instanceof \PhpParser\Node\Expr\FuncCall) {
+		assertType('PhpParser\Node\Expr\FuncCall', $node);
+		assertType('PhpParser\Node\Expr', $node->name);
+	}
+}
+
+class FooContainer {
+	/** @var \stdClass|string */
+	public $x;
+	/** @var \stdClass|int */
+	public $y;
+}
+
+function fooPropertyFetchInstanceof(FooContainer $c): void {
+	if ($c->x instanceof \stdClass && $c->y instanceof \stdClass) {
+		return;
+	}
+	if ($c->x instanceof \stdClass) {
+		assertType('int', $c->y);
+	}
+}
+
+function fooPropertyFetchInstanceofOr(FooContainer $c): void {
+	if (!$c->x instanceof \stdClass || !$c->y instanceof \stdClass) {
+		if ($c->x instanceof \stdClass) {
+			assertType('int', $c->y);
+		}
+		return;
+	}
+	assertType('stdClass', $c->x);
+	assertType('stdClass', $c->y);
+}
diff --git a/tests/PHPStan/Analyser/nsrt/bug-7716.php b/tests/PHPStan/Analyser/nsrt/bug-7716.php
index 63280c3b46..bd4d38f66e 100644
--- a/tests/PHPStan/Analyser/nsrt/bug-7716.php
+++ b/tests/PHPStan/Analyser/nsrt/bug-7716.php
@@ -15,13 +15,13 @@ public function sayHello(array $array): int
 		$hasBar = isset($array['bar']) && $array['bar'] > 1;
 
 		if ($hasFoo) {
-			assertType('array{foo: int, bar?: int}', $array);
+			assertType('array{foo: int<2, max>, bar?: int}', $array);
 			assertType('int<2, max>', $array['foo']);
 			return $array['foo'];
 		}
 
 		if ($hasBar) {
-			assertType('array{foo?: int, bar: int}', $array);
+			assertType('array{foo?: int, bar: int<2, max>}', $array);
 			assertType('int<2, max>', $array['bar']);
 			return $array['bar'];
 		}
@@ -38,13 +38,13 @@ public function sayHello2(array $array): int
 		$hasFoo = isset($array['foo']) && $array['foo'] > 1;
 
 		if ($hasFoo) {
-			assertType('array{foo: int, bar?: int}', $array);
+			assertType('array{foo: int<2, max>, bar?: int}', $array);
 			assertType('int<2, max>', $array['foo']);
 			return $array['foo'];
 		}
 
 		if ($hasBar) {
-			assertType('array{foo?: int, bar: int}', $array);
+			assertType('array{foo?: int, bar: int<2, max>}', $array);
 			assertType('int<2, max>', $array['bar']);
 			return $array['bar'];
 		}