diff --git a/src/Analyser/SpecifiedTypes.php b/src/Analyser/SpecifiedTypes.php
index 92963fb826..0feb361336 100644
--- a/src/Analyser/SpecifiedTypes.php
+++ b/src/Analyser/SpecifiedTypes.php
@@ -58,28 +58,31 @@ public function getNewConditionalExpressionHolders(): array
 	/** @api */
 	public function intersectWith(SpecifiedTypes $other): self
 	{
+		$normalized = $this->normalize();
+		$otherNormalized = $other->normalize();
+
 		$sureTypeUnion = [];
 		$sureNotTypeUnion = [];
 
-		foreach ($this->sureTypes as $exprString => [$exprNode, $type]) {
-			if (!isset($other->sureTypes[$exprString])) {
+		foreach ($normalized->sureTypes as $exprString => [$exprNode, $type]) {
+			if (!isset($otherNormalized->sureTypes[$exprString])) {
 				continue;
 			}
 
 			$sureTypeUnion[$exprString] = [
 				$exprNode,
-				TypeCombinator::union($type, $other->sureTypes[$exprString][1]),
+				TypeCombinator::union($type, $otherNormalized->sureTypes[$exprString][1]),
 			];
 		}
 
-		foreach ($this->sureNotTypes as $exprString => [$exprNode, $type]) {
-			if (!isset($other->sureNotTypes[$exprString])) {
+		foreach ($normalized->sureNotTypes as $exprString => [$exprNode, $type]) {
+			if (!isset($otherNormalized->sureNotTypes[$exprString])) {
 				continue;
 			}
 
 			$sureNotTypeUnion[$exprString] = [
 				$exprNode,
-				TypeCombinator::intersect($type, $other->sureNotTypes[$exprString][1]),
+				TypeCombinator::intersect($type, $otherNormalized->sureNotTypes[$exprString][1]),
 			];
 		}
 
@@ -117,4 +120,26 @@ public function unionWith(SpecifiedTypes $other): self
 		return new self($sureTypeUnion, $sureNotTypeUnion);
 	}
 
+	public function inverse(): self
+	{
+		return new self($this->sureNotTypes, $this->sureTypes, $this->overwrite, $this->newConditionalExpressionHolders);
+	}
+
+	private function normalize(): self
+	{
+		$sureTypes = $this->sureTypes;
+		$sureNotTypes = [];
+
+		foreach ($this->sureNotTypes as $exprString => [$exprNode, $sureNotType]) {
+			if (!isset($sureTypes[$exprString])) {
+				$sureNotTypes[$exprString] = [$exprNode, $sureNotType];
+				continue;
+			}
+
+			$sureTypes[$exprString][1] = TypeCombinator::remove($sureTypes[$exprString][1], $sureNotType);
+		}
+
+		return new self($sureTypes, $sureNotTypes, $this->overwrite, $this->newConditionalExpressionHolders);
+	}
+
 }
diff --git a/src/Analyser/TypeSpecifier.php b/src/Analyser/TypeSpecifier.php
index b59275d157..44bc014119 100644
--- a/src/Analyser/TypeSpecifier.php
+++ b/src/Analyser/TypeSpecifier.php
@@ -666,8 +666,12 @@ public function specifyTypesInCondition(
 
 			return $this->handleDefaultTruthyOrFalseyContext($context, $expr, $scope);
 		} elseif ($expr instanceof BooleanAnd || $expr instanceof LogicalAnd) {
+			if (!$scope instanceof MutatingScope) {
+				throw new ShouldNotHappenException();
+			}
 			$leftTypes = $this->specifyTypesInCondition($scope, $expr->left, $context);
-			$rightTypes = $this->specifyTypesInCondition($scope, $expr->right, $context);
+			$leftScope = $scope->filterBySpecifiedTypes($context->true() ? $leftTypes : $leftTypes->inverse());
+			$rightTypes = $this->specifyTypesInCondition($leftScope, $expr->right, $context);
 			$types = $context->true() ? $leftTypes->unionWith($rightTypes) : $leftTypes->intersectWith($rightTypes);
 			if ($context->false()) {
 				return new SpecifiedTypes(
@@ -683,8 +687,12 @@ public function specifyTypesInCondition(
 
 			return $types;
 		} elseif ($expr instanceof BooleanOr || $expr instanceof LogicalOr) {
+			if (!$scope instanceof MutatingScope) {
+				throw new ShouldNotHappenException();
+			}
 			$leftTypes = $this->specifyTypesInCondition($scope, $expr->left, $context);
-			$rightTypes = $this->specifyTypesInCondition($scope, $expr->right, $context);
+			$leftScope = $scope->filterBySpecifiedTypes($context->true() ? $leftTypes->inverse() : $leftTypes);
+			$rightTypes = $this->specifyTypesInCondition($leftScope, $expr->right, $context);
 			$types = $context->true() ? $leftTypes->intersectWith($rightTypes) : $leftTypes->unionWith($rightTypes);
 			if ($context->true()) {
 				return new SpecifiedTypes(
diff --git a/tests/PHPStan/Analyser/NodeScopeResolverTest.php b/tests/PHPStan/Analyser/NodeScopeResolverTest.php
index 3535aac6dc..0795d0586b 100644
--- a/tests/PHPStan/Analyser/NodeScopeResolverTest.php
+++ b/tests/PHPStan/Analyser/NodeScopeResolverTest.php
@@ -692,6 +692,7 @@ public function dataFileAsserts(): iterable
 		if (PHP_VERSION_ID >= 80000) {
 			yield from $this->gatherAssertTypes(__DIR__ . '/data/bug-6308.php');
 		}
+		yield from $this->gatherAssertTypes(__DIR__ . '/data/bug-6329.php');
 
 		if (PHP_VERSION_ID >= 70400) {
 			yield from $this->gatherAssertTypes(__DIR__ . '/../Rules/Comparison/data/bug-6473.php');
diff --git a/tests/PHPStan/Analyser/TypeSpecifierTest.php b/tests/PHPStan/Analyser/TypeSpecifierTest.php
index 7c8aa8986b..d86f095c54 100644
--- a/tests/PHPStan/Analyser/TypeSpecifierTest.php
+++ b/tests/PHPStan/Analyser/TypeSpecifierTest.php
@@ -8,6 +8,7 @@
 use PhpParser\Node\Expr\BinaryOp\Identical;
 use PhpParser\Node\Expr\BinaryOp\NotIdentical;
 use PhpParser\Node\Expr\BooleanNot;
+use PhpParser\Node\Expr\ConstFetch;
 use PhpParser\Node\Expr\FuncCall;
 use PhpParser\Node\Expr\PropertyFetch;
 use PhpParser\Node\Expr\Variable;
@@ -965,6 +966,62 @@ public function dataCondition(): array
 				],
 				[],
 			],
+			[
+				new Expr\BinaryOp\BooleanOr(
+					new Expr\BinaryOp\BooleanAnd(
+						$this->createFunctionCall('is_string', 'a'),
+						new NotIdentical(new String_(''), new Variable('a')),
+					),
+					new Identical(new Expr\ConstFetch(new Name('null')), new Variable('a')),
+				),
+				['$a' => 'non-empty-string|null'],
+				['$a' => '~null'],
+			],
+			[
+				new Expr\BinaryOp\BooleanOr(
+					new Expr\BinaryOp\BooleanAnd(
+						$this->createFunctionCall('is_string', 'a'),
+						new Expr\BinaryOp\Greater(
+							$this->createFunctionCall('strlen', 'a'),
+							new LNumber(0),
+						),
+					),
+					new Identical(new Expr\ConstFetch(new Name('null')), new Variable('a')),
+				),
+				['$a' => 'non-empty-string|null'],
+				['$a' => '~non-empty-string|null'],
+			],
+			[
+				new Expr\BinaryOp\BooleanOr(
+					new Expr\BinaryOp\BooleanAnd(
+						$this->createFunctionCall('is_array', 'a'),
+						new Expr\BinaryOp\Greater(
+							$this->createFunctionCall('count', 'a'),
+							new LNumber(0),
+						),
+					),
+					new Identical(new Expr\ConstFetch(new Name('null')), new Variable('a')),
+				),
+				['$a' => 'non-empty-array|null'],
+				['$a' => '~non-empty-array|null'],
+			],
+			[
+				new Expr\BinaryOp\BooleanAnd(
+					$this->createFunctionCall('is_array', 'foo'),
+					new Identical(
+						new FuncCall(
+							new Name('array_filter'),
+							[new Arg(new Variable('foo')), new Arg(new String_('is_string')), new Arg(new ConstFetch(new Name('ARRAY_FILTER_USE_KEY')))],
+						),
+						new Variable('foo'),
+					),
+				),
+				[
+					'$foo' => 'array<string, mixed>',
+					'array_filter($foo, \'is_string\', ARRAY_FILTER_USE_KEY)' => 'array<string, mixed>',
+				],
+				[],
+			],
 		];
 	}
 
diff --git a/tests/PHPStan/Analyser/data/bug-6329.php b/tests/PHPStan/Analyser/data/bug-6329.php
new file mode 100644
index 0000000000..c6b49e87e4
--- /dev/null
+++ b/tests/PHPStan/Analyser/data/bug-6329.php
@@ -0,0 +1,185 @@
+<?php
+
+namespace Bug6329;
+
+use function PHPStan\Testing\assertType;
+
+/**
+ * @param mixed $a
+ */
+function nonEmptyString1($a): void
+{
+	if (is_string($a) && '' !== $a || null === $a) {
+		assertType('non-empty-string|null', $a);
+	}
+
+	if ('' !== $a && is_string($a) || null === $a) {
+		assertType('non-empty-string|null', $a);
+	}
+
+	if (null === $a || is_string($a) && '' !== $a) {
+		assertType('non-empty-string|null', $a);
+	}
+
+	if (null === $a || '' !== $a && is_string($a)) {
+		assertType('non-empty-string|null', $a);
+	}
+}
+
+/**
+ * @param mixed $a
+ */
+function nonEmptyString2($a): void
+{
+	if (is_string($a) && strlen($a) > 0 || null === $a) {
+		assertType('non-empty-string|null', $a);
+	}
+
+	if (null === $a || is_string($a) && strlen($a) > 0) {
+		assertType('non-empty-string|null', $a);
+	}
+}
+
+
+/**
+ * @param mixed $a
+ */
+function int1($a): void
+{
+	if (is_int($a) && 0 !== $a || null === $a) {
+		assertType('int<min, -1>|int<1, max>|null', $a);
+	}
+
+	if (0 !== $a && is_int($a) || null === $a) {
+		assertType('int<min, -1>|int<1, max>|null', $a);
+	}
+
+	if (null === $a || is_int($a) && 0 !== $a) {
+		assertType('int<min, -1>|int<1, max>|null', $a);
+	}
+
+	if (null === $a || 0 !== $a && is_int($a)) {
+		assertType('int<min, -1>|int<1, max>|null', $a);
+	}
+}
+
+/**
+ * @param mixed $a
+ */
+function int2($a): void
+{
+	if (is_int($a) && $a > 0 || null === $a) {
+		assertType('int<1, max>|null', $a);
+	}
+
+	if (null === $a || is_int($a) && $a > 0) {
+		assertType('int<1, max>|null', $a);
+	}
+}
+
+
+/**
+ * @param mixed $a
+ */
+function true($a): void
+{
+	if (is_bool($a) && false !== $a || null === $a) {
+		assertType('true|null', $a);
+	}
+
+	if (false !== $a && is_bool($a) || null === $a) {
+		assertType('true|null', $a);
+	}
+
+	if (null === $a || is_bool($a) && false !== $a) {
+		assertType('true|null', $a);
+	}
+
+	if (null === $a || false !== $a && is_bool($a)) {
+		assertType('true|null', $a);
+	}
+}
+
+/**
+ * @param mixed $a
+ */
+function nonEmptyArray1($a): void
+{
+	if (is_array($a) && [] !== $a || null === $a) {
+		assertType('non-empty-array|null', $a);
+	}
+
+	if ([] !== $a && is_array($a) || null === $a) {
+		assertType('non-empty-array|null', $a);
+	}
+
+	if (null === $a || is_array($a) && [] !== $a) {
+		assertType('non-empty-array|null', $a);
+	}
+
+	if (null === $a || [] !== $a && is_array($a)) {
+		assertType('non-empty-array|null', $a);
+	}
+}
+
+/**
+ * @param mixed $a
+ */
+function nonEmptyArray2($a): void
+{
+	if (is_array($a) && count($a) > 0 || null === $a) {
+		assertType('non-empty-array|null', $a);
+	}
+
+	if (null === $a || is_array($a) && count($a) > 0) {
+		assertType('non-empty-array|null', $a);
+	}
+}
+
+/**
+ * @param mixed $a
+ * @param mixed $b
+ * @param mixed $c
+ */
+function inverse($a, $b, $c): void
+{
+	if ((!is_string($a) || '' === $a) && null !== $a) {
+	} else {
+		assertType('non-empty-string|null', $a);
+	}
+
+	if ((!is_int($b) || $b <= 0) && null !== $b) {
+	} else {
+		assertType('int<1, max>|null', $b);
+	}
+
+	if (null !== $c && (!is_array($c) || count($c) <= 0)) {
+	} else {
+		assertType('non-empty-array|null', $c);
+	}
+}
+
+/**
+ * @param mixed $a
+ * @param mixed $b
+ * @param mixed $c
+ * @param mixed $d
+ */
+function combinations($a, $b, $c, $d): void
+{
+	if (is_string($a) && '' !== $a || is_int($a) && $a > 0 || null === $a) {
+		assertType('int<1, max>|non-empty-string|null', $a);
+	}
+	if ((!is_string($b) || '' === $b) && (!is_int($b) || $b <= 0) && null !== $b) {
+	} else {
+		assertType('int<1, max>|non-empty-string|null', $b);
+	}
+
+	if (is_array($c) && $c === array_filter($c, 'is_string', ARRAY_FILTER_USE_KEY) || null === $c) {
+		assertType('array<string, mixed>|null', $c);
+	}
+	if ((!is_array($d) || $d !== array_filter($d, 'is_string', ARRAY_FILTER_USE_KEY)) && null !== $d) {
+	} else {
+		assertType('array<string, mixed>|null', $d);
+	}
+}