diff --git a/src/Analyser/LegacyTypeSpecifier.php b/src/Analyser/LegacyTypeSpecifier.php
index aadef4281e..c2cfa70c73 100644
--- a/src/Analyser/LegacyTypeSpecifier.php
+++ b/src/Analyser/LegacyTypeSpecifier.php
@@ -38,6 +38,7 @@
 use PHPStan\Type\Accessory\AccessoryNonEmptyStringType;
 use PHPStan\Type\Accessory\AccessoryNonFalsyStringType;
 use PHPStan\Type\Accessory\HasOffsetType;
+use PHPStan\Type\Accessory\HasOffsetValueType;
 use PHPStan\Type\Accessory\HasPropertyType;
 use PHPStan\Type\Accessory\NonEmptyArrayType;
 use PHPStan\Type\ArrayType;
@@ -92,6 +93,8 @@
 final class LegacyTypeSpecifier implements TypeSpecifier
 {
 
+	private const MAX_ACCESSORIES_LIMIT = 8;
+
 	/** @var MethodTypeSpecifyingExtension[][]|null */
 	private ?array $methodTypeSpecifyingExtensionsByClass = null;
 
@@ -1189,7 +1192,27 @@ private function specifyTypesForCountFuncCall(
 						$builderData[] = [$offsetType, $arrayType->getOffsetValueType($offsetType), !$hasOffset->yes()];
 					}
 				} else {
-					$resultTypes[] = TypeCombinator::intersect($arrayType, new NonEmptyArrayType());
+					$intersection = [];
+					$intersection[] = $arrayType;
+					$intersection[] = new NonEmptyArrayType();
+
+					$zero = new ConstantIntegerType(0);
+					$i = 0;
+					foreach ($builderData as [$offsetType, $valueType]) {
+						// non-empty-list already implies the offset 0
+						if ($zero->isSuperTypeOf($offsetType)->yes()) {
+							continue;
+						}
+
+						if ($i > self::MAX_ACCESSORIES_LIMIT) {
+							break;
+						}
+
+						$intersection[] = new HasOffsetValueType($offsetType, $valueType);
+						$i++;
+					}
+
+					$resultTypes[] = TypeCombinator::intersect(...$intersection);
 					continue;
 				}
 
diff --git a/src/Type/IntersectionType.php b/src/Type/IntersectionType.php
index cd66832682..3aa4a9a2d8 100644
--- a/src/Type/IntersectionType.php
+++ b/src/Type/IntersectionType.php
@@ -691,6 +691,10 @@ public function getArraySize(): Type
 			$knownOffsets[$type->getOffsetType()->getValue()] = true;
 		}
 
+		if ($this->isList()->yes() && $this->isIterableAtLeastOnce()->yes()) {
+			$knownOffsets[0] = true;
+		}
+
 		if ($knownOffsets !== []) {
 			return TypeCombinator::intersect($arraySize, IntegerRangeType::fromInterval(count($knownOffsets), null));
 		}
@@ -830,9 +834,26 @@ public function isOffsetAccessLegal(): TrinaryLogic
 
 	public function hasOffsetValueType(Type $offsetType): TrinaryLogic
 	{
-		if ($this->isList()->yes() && $this->isIterableAtLeastOnce()->yes()) {
+		if ($this->isList()->yes()) {
 			$arrayKeyOffsetType = $offsetType->toArrayKey();
-			if ((new ConstantIntegerType(0))->isSuperTypeOf($arrayKeyOffsetType)->yes()) {
+
+			$negative = IntegerRangeType::fromInterval(null, -1);
+			if ($negative->isSuperTypeOf($arrayKeyOffsetType)->yes()) {
+				return TrinaryLogic::createNo();
+			}
+
+			$size = $this->getArraySize();
+			if ($size instanceof IntegerRangeType && $size->getMin() !== null) {
+				$knownOffsets = IntegerRangeType::fromInterval(0, $size->getMin() - 1);
+			} elseif ($size instanceof ConstantIntegerType) {
+				$knownOffsets = IntegerRangeType::fromInterval(0, $size->getValue() - 1);
+			} elseif ($this->isIterableAtLeastOnce()->yes()) {
+				$knownOffsets = new ConstantIntegerType(0);
+			} else {
+				$knownOffsets = null;
+			}
+
+			if ($knownOffsets !== null && $knownOffsets->isSuperTypeOf($arrayKeyOffsetType)->yes()) {
 				return TrinaryLogic::createYes();
 			}
 
diff --git a/tests/PHPStan/Analyser/nsrt/bug-11642.php b/tests/PHPStan/Analyser/nsrt/bug-11642.php
index 520cf772bf..7c72706fe5 100644
--- a/tests/PHPStan/Analyser/nsrt/bug-11642.php
+++ b/tests/PHPStan/Analyser/nsrt/bug-11642.php
@@ -34,6 +34,7 @@ function doFoo() {
 	if (count($entries) !== count($payload->ids)) {
 		exit();
 	}
+	assertType('int<1, max>', count($entries));
 
 	assertType('non-empty-list<stdClass>', $entries);
 	if (count($entries) > 3) {
diff --git a/tests/PHPStan/Analyser/nsrt/bug-13747.php b/tests/PHPStan/Analyser/nsrt/bug-13747.php
new file mode 100644
index 0000000000..e8a033f170
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-13747.php
@@ -0,0 +1,99 @@
+<?php declare(strict_types = 1);
+
+namespace Bug13747;
+
+use function PHPStan\Testing\assertType;
+
+class HelloWorld
+{
+	/** @param list<int> $list */
+	public function count($list): void
+	{
+		if (count($list) === 0) {
+			return;
+		}
+
+		if (count($list) > 2) {
+			assertType('false', array_key_exists(-1, $list));
+			assertType('true', array_key_exists(0, $list));
+			assertType('true', array_key_exists(1, $list));
+			assertType('true', array_key_exists(2, $list));
+			assertType('bool', array_key_exists(3, $list));
+
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)&hasOffsetValue(2, int)', $list);
+			assertType('int<3, max>', count($list));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+		assertType('non-empty-list<int>', $list);
+
+		if (count($list, COUNT_NORMAL) > 2) {
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)&hasOffsetValue(2, int)', $list);
+			assertType('int<3, max>', count($list, COUNT_NORMAL));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+
+		assertType('non-empty-list<int>', $list);
+		if (count($list, COUNT_RECURSIVE) > 2) { // COUNT_RECURSIVE on non-recursive array
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)&hasOffsetValue(2, int)', $list);
+			assertType('int<3, max>', count($list, COUNT_RECURSIVE));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+	}
+
+	/** @param list<int> $list */
+	public function doFoo($list): void
+	{
+		if (count($list) === 0) {
+			return;
+		}
+
+		if (count($list) >= 2) {
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)', $list);
+			assertType('int<2, max>', count($list));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+	}
+
+	/** @param list<int> $list */
+	public function doBar($list): void
+	{
+		if (count($list) === 0) {
+			return;
+		}
+
+		if (2 <= count($list)) {
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)', $list);
+			assertType('int<2, max>', count($list));
+		} else {
+			assertType('non-empty-list<int>', $list);
+			assertType('1', count($list));
+		}
+	}
+
+	/** @param list<int> $list */
+	public function checkLimit($list): void
+	{
+		if (count($list) === 0) {
+			return;
+		}
+
+		if (count($list) > 9) {
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)&hasOffsetValue(2, int)&hasOffsetValue(3, int)&hasOffsetValue(4, int)&hasOffsetValue(5, int)&hasOffsetValue(6, int)&hasOffsetValue(7, int)&hasOffsetValue(8, int)&hasOffsetValue(9, int)', $list);
+			assertType('int<10, max>', count($list));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+
+		if (count($list) > 10) {
+			assertType('non-empty-list<int>&hasOffsetValue(1, int)&hasOffsetValue(2, int)&hasOffsetValue(3, int)&hasOffsetValue(4, int)&hasOffsetValue(5, int)&hasOffsetValue(6, int)&hasOffsetValue(7, int)&hasOffsetValue(8, int)&hasOffsetValue(9, int)', $list);
+			assertType('int<11, max>', count($list));
+		} else {
+			assertType('non-empty-list<int>', $list);
+		}
+
+	}
+}
diff --git a/tests/PHPStan/Analyser/nsrt/count-recursive.php b/tests/PHPStan/Analyser/nsrt/count-recursive.php
index 1725b929fd..b8539e54da 100644
--- a/tests/PHPStan/Analyser/nsrt/count-recursive.php
+++ b/tests/PHPStan/Analyser/nsrt/count-recursive.php
@@ -84,8 +84,8 @@ public function countList($list): void
 	{
 		if (count($list) > 2) {
 			assertType('int<3, max>', count($list));
-			assertType('int<1, max>', count($list, COUNT_NORMAL));
-			assertType('int<1, max>', count($list, COUNT_RECURSIVE));
+			assertType('int<3, max>', count($list, COUNT_NORMAL));
+			assertType('int<3, max>', count($list, COUNT_RECURSIVE));
 		}
 	}
 
@@ -93,9 +93,9 @@ public function countList($list): void
 	public function countListNormal($list): void
 	{
 		if (count($list, COUNT_NORMAL) > 2) {
-			assertType('int<1, max>', count($list));
+			assertType('int<3, max>', count($list));
 			assertType('int<3, max>', count($list, COUNT_NORMAL));
-			assertType('int<1, max>', count($list, COUNT_RECURSIVE));
+			assertType('int<3, max>', count($list, COUNT_RECURSIVE));
 		}
 	}
 
@@ -124,8 +124,8 @@ public function countMixed($arr, $mode): void
 	public function countListRecursive($list): void
 	{
 		if (count($list, COUNT_RECURSIVE) > 2) {
-			assertType('int<1, max>', count($list));
-			assertType('int<1, max>', count($list, COUNT_NORMAL));
+			assertType('int<3, max>', count($list));
+			assertType('int<3, max>', count($list, COUNT_NORMAL));
 			assertType('int<3, max>', count($list, COUNT_RECURSIVE));
 		}
 	}