diff --git a/src/Type/ArrayType.php b/src/Type/ArrayType.php
index a951f13c24..895f07ae6f 100644
--- a/src/Type/ArrayType.php
+++ b/src/Type/ArrayType.php
@@ -147,8 +147,19 @@ public function accepts(Type $type, bool $strictTypes): AcceptsResult
 	public function isSuperTypeOf(Type $type): IsSuperTypeOfResult
 	{
 		if ($type instanceof self || $type instanceof ConstantArrayType) {
-			return $this->getItemType()->isSuperTypeOf($type->getItemType())
+			$result = $this->getItemType()->isSuperTypeOf($type->getItemType())
 				->and($this->getIterableKeyType()->isSuperTypeOf($type->getIterableKeyType()));
+			if (
+				$result->no()
+				&& $type->isConstantArray()->yes()
+				&& !$type->isIterableAtLeastOnce()->yes()
+			) {
+				// A possibly-empty constant array always admits the empty array,
+				// which is a subtype of every array type, so the relationship can
+				// only be "maybe", never a definite "no".
+				return IsSuperTypeOfResult::createMaybe();
+			}
+			return $result;
 		}
 
 		if ($type instanceof CompoundType) {
diff --git a/src/Type/Constant/ConstantArrayType.php b/src/Type/Constant/ConstantArrayType.php
index 7eca2eaa58..272cbec8da 100644
--- a/src/Type/Constant/ConstantArrayType.php
+++ b/src/Type/Constant/ConstantArrayType.php
@@ -1437,6 +1437,57 @@ public function unsetOffset(Type $offsetType, bool $preserveListCertainty = fals
 		return $this->recreate($this->keyTypes, $this->valueTypes, $this->nextAutoIndexes, $optionalKeys, $newIsList, $this->unsealed);
 	}
 
+	/**
+	 * Compute the list-ness trinary of a sealed array shape purely from its keys
+	 * and their optionality: `yes` if every realization (choice of which optional
+	 * keys are present) is a list, `no` if none is, `maybe` otherwise. An optional
+	 * key that breaks list-ness only degrades the answer to `maybe`, because the
+	 * realization where that key is absent may still be a list.
+	 *
+	 * @param list<ConstantIntegerType|ConstantStringType> $keyTypes
+	 * @param int[] $optionalKeys
+	 */
+	private static function inferIsListFromShape(array $keyTypes, array $optionalKeys): TrinaryLogic
+	{
+		$optional = [];
+		foreach ($optionalKeys as $optionalKey) {
+			$optional[$optionalKey] = true;
+		}
+
+		// Prefix lengths reachable by realizations that are still a valid list.
+		$validLengths = [0 => true];
+		$existsInvalid = false;
+
+		foreach ($keyTypes as $i => $keyType) {
+			$isOptional = array_key_exists($i, $optional);
+			$value = $keyType instanceof ConstantIntegerType ? $keyType->getValue() : null;
+
+			$newValidLengths = [];
+			foreach (array_keys($validLengths) as $length) {
+				if ($isOptional) {
+					// Skipping the key keeps the realization a valid list prefix.
+					$newValidLengths[$length] = true;
+				}
+
+				if ($value === $length) {
+					// Including the key extends the list into the next slot.
+					$newValidLengths[$length + 1] = true;
+				} else {
+					// Including a non-sequential key yields a non-list realization.
+					$existsInvalid = true;
+				}
+			}
+
+			$validLengths = $newValidLengths;
+			if ($validLengths === []) {
+				// No realization can be a list from here on.
+				return TrinaryLogic::createNo();
+			}
+		}
+
+		return $existsInvalid ? TrinaryLogic::createMaybe() : TrinaryLogic::createYes();
+	}
+
 	/**
 	 * When we're unsetting something not on the array, it will be untouched,
 	 * So the nextAutoIndexes won't change, and the array might still be a list even with PHPStan definition.
@@ -3032,12 +3083,23 @@ public function mergeWith(self $otherArray): self
 		/** @var list<ConstantIntegerType|ConstantStringType> $keyTypes */
 		$keyTypes = $keyTypes;
 
+		// A key present on only one side becomes optional, so a sealed result may gain
+		// list realizations (e.g. the empty array) the naive `and` misses; fold in the
+		// list-ness recomputed from the merged shape. `or` keeps a naive `yes` (two
+		// lists merge into a list even where the shape's independent-optional reading
+		// would say maybe) while letting the shape lift a `no`/`maybe`.
+		$naiveIsList = $this->isList->and($otherArray->isList);
+		$mergedIsSealed = $mergedUnsealedKey instanceof NeverType && $mergedUnsealedKey->isExplicit();
+		$isList = $mergedIsSealed
+			? $naiveIsList->or(self::inferIsListFromShape($keyTypes, $optionalKeys))
+			: $naiveIsList;
+
 		return $this->recreate(
 			$keyTypes,
 			$valueTypes,
 			$nextAutoIndexes,
 			$optionalKeys,
-			$this->isList->and($otherArray->isList),
+			$isList,
 			$resultUnsealed,
 		);
 	}
@@ -3064,7 +3126,20 @@ private function legacyMergeWith(self $otherArray): self
 		$nextAutoIndexes = array_values(array_unique(array_merge($this->nextAutoIndexes, $otherArray->nextAutoIndexes)));
 		sort($nextAutoIndexes);
 
-		return $this->recreate($this->keyTypes, $valueTypes, $nextAutoIndexes, $optionalKeys, $this->isList->and($otherArray->isList), $this->unsealed);
+		// This path keeps only `$this`'s keys, widening those missing from the other
+		// side to optional, so a sealed result may gain list realizations the naive
+		// `and` misses — including lifting a `maybe` back to `yes` when the widened
+		// keys form a valid list suffix. Fold in the list-ness of the merged shape;
+		// `or` keeps a naive `yes` unchanged, and an unsealed result can't be
+		// re-derived from the known keys alone.
+		$naiveIsList = $this->isList->and($otherArray->isList);
+		$mergedIsSealed = $this->unsealed === null
+			|| ($this->unsealed[0] instanceof NeverType && $this->unsealed[0]->isExplicit());
+		$isList = $mergedIsSealed
+			? $naiveIsList->or(self::inferIsListFromShape($this->keyTypes, $optionalKeys))
+			: $naiveIsList;
+
+		return $this->recreate($this->keyTypes, $valueTypes, $nextAutoIndexes, $optionalKeys, $isList, $this->unsealed);
 	}
 
 	/**
@@ -3168,6 +3243,39 @@ public function makeList(): Type
 			return new NeverType();
 		}
 
+		// isList is Maybe: some values are lists, some are not. When the shape
+		// is sealed, a key sitting past a gap in the 0..n sequence (or any
+		// non-integer key) can never appear in a list, so keep only the
+		// contiguous 0..m prefix. Unsealed extras may fill such gaps, so there
+		// every key is kept.
+		if ($this->isUnsealed()->no()) {
+			$positionByIndex = [];
+			foreach ($this->keyTypes as $position => $keyType) {
+				if (!$keyType instanceof ConstantIntegerType) {
+					continue;
+				}
+				$positionByIndex[$keyType->getValue()] = $position;
+			}
+
+			$keptPositions = [];
+			for ($index = 0; array_key_exists($index, $positionByIndex); $index++) {
+				$keptPositions[] = $positionByIndex[$index];
+			}
+
+			if (count($keptPositions) < count($this->keyTypes)) {
+				$builder = ConstantArrayTypeBuilder::createEmpty();
+				foreach ($keptPositions as $position) {
+					$builder->setOffsetValueType(
+						$this->keyTypes[$position],
+						$this->valueTypes[$position],
+						$this->isOptionalKey($position),
+					);
+				}
+
+				return $builder->getArray();
+			}
+		}
+
 		return $this->recreate($this->keyTypes, $this->valueTypes, $this->nextAutoIndexes, $this->optionalKeys, TrinaryLogic::createYes(), $this->unsealed);
 	}
 
diff --git a/src/Type/Constant/ConstantArrayTypeBuilder.php b/src/Type/Constant/ConstantArrayTypeBuilder.php
index e81a4d694e..aa24969c83 100644
--- a/src/Type/Constant/ConstantArrayTypeBuilder.php
+++ b/src/Type/Constant/ConstantArrayTypeBuilder.php
@@ -224,11 +224,11 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $opt
 								if ($offsetValue <= $max) {
 									$this->isList = $this->isList->and(TrinaryLogic::createMaybe());
 								} else {
-									$this->isList = TrinaryLogic::createNo();
+									$this->markNonListKey($optional);
 								}
 							}
 						} else {
-							$this->isList = TrinaryLogic::createNo();
+							$this->markNonListKey($optional);
 						}
 
 						if ($offsetValue >= $max) {
@@ -245,10 +245,10 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $opt
 							}
 						}
 					} else {
-						$this->isList = TrinaryLogic::createNo();
+						$this->markNonListKey($optional);
 					}
 				} else {
-					$this->isList = TrinaryLogic::createNo();
+					$this->markNonListKey($optional);
 				}
 
 				if ($optional) {
@@ -410,6 +410,20 @@ public function setOffsetValueType(?Type $offsetType, Type $valueType, bool $opt
 		$this->degradeToGeneralArray = true;
 	}
 
+	/**
+	 * Record that a key incompatible with list ordering was added.
+	 *
+	 * A required key definitely breaks list-ness. An optional key only might
+	 * be present, so the array is still a list whenever the key is absent —
+	 * degrade Yes to Maybe rather than to No (No stays No).
+	 */
+	private function markNonListKey(bool $optional): void
+	{
+		$this->isList = $optional
+			? $this->isList->and(TrinaryLogic::createMaybe())
+			: TrinaryLogic::createNo();
+	}
+
 	public function degradeToGeneralArray(bool $oversized = false): void
 	{
 		if ($this->disableArrayDegradation) {
diff --git a/tests/PHPStan/Analyser/nsrt/array-shape-list-optional.php b/tests/PHPStan/Analyser/nsrt/array-shape-list-optional.php
index 156ad93ed2..9acad79f69 100644
--- a/tests/PHPStan/Analyser/nsrt/array-shape-list-optional.php
+++ b/tests/PHPStan/Analyser/nsrt/array-shape-list-optional.php
@@ -25,8 +25,11 @@ public function doFoo(
 		assertType('list{0: string, 1: int, 2?: string, 3?: string}', $valid1);
 		assertType('list{0: string, 1?: int, 2?: string, 3?: string}', $valid2);
 		assertType('non-empty-array{0?: string, 1?: int, 2?: string, 3?: string}', $valid3);
-		assertType('*NEVER*', $invalid1);
-		assertType('*NEVER*', $invalid2);
+		// The trailing keys can never appear in a list (4 sits past the gap at
+		// 3; foo is not an integer), so they are dropped, leaving the valid
+		// list projection rather than an empty *NEVER*.
+		assertType('array{0: string, 1: int, 2?: string}', $invalid1);
+		assertType('array{0: string, 1: int, 2?: string}', $invalid2);
 	}
 
 }
diff --git a/tests/PHPStan/Analyser/nsrt/bug-14938.php b/tests/PHPStan/Analyser/nsrt/bug-14938.php
new file mode 100644
index 0000000000..882b70b8ac
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/bug-14938.php
@@ -0,0 +1,86 @@
+<?php
+
+namespace Bug14938;
+
+use function PHPStan\Testing\assertType;
+
+class Foo
+{
+
+	/**
+	 * @param array{a?: string} $optStr
+	 * @param array{0: int, a?: string} $listPlusOptStr
+	 * @param array{-1?: string} $optNeg
+	 * @param array{0: int, 5?: string} $listPlusGap
+	 * @param array{a: string} $reqStr
+	 * @param array{1: string} $gapReq
+	 * @param array{0?: string} $optZero
+	 */
+	public function doFoo(
+		array $optStr,
+		array $listPlusOptStr,
+		array $optNeg,
+		array $listPlusGap,
+		array $reqStr,
+		array $gapReq,
+		array $optZero,
+	): void
+	{
+		// An optional non-list key might be absent, so the array can still be
+		// a list ([] / the list prefix) — array_is_list() is not decidable.
+		assertType('bool', array_is_list($optStr));
+		assertType('bool', array_is_list($listPlusOptStr));
+		assertType('bool', array_is_list($optNeg));
+		assertType('bool', array_is_list($listPlusGap));
+
+		// A required non-list key is always present, so it is never a list.
+		assertType('false', array_is_list($reqStr));
+		assertType('false', array_is_list($gapReq));
+
+		// Only an optional key 0 keeps it a guaranteed list ([] and [v]).
+		assertType('true', array_is_list($optZero));
+	}
+
+	/**
+	 * @param array{a?: string} $optStr
+	 */
+	public function narrowing(array $optStr): void
+	{
+		if (array_is_list($optStr)) {
+			assertType('list{}&list', $optStr);
+		} else {
+			// array_is_list()'s false branch is not narrowed, so `a` stays optional
+			// here rather than being refined to array{a: string}.
+			assertType('array{a?: string}', $optStr);
+		}
+	}
+
+	public function mergedShapes(): void
+	{
+		// Merging a list with a shape that adds a string key: the empty-of-the-extra
+		// realization is still a list, so array_is_list() is not decidable.
+		$a = [0 => 'z'];
+		if (rand(0, 1)) {
+			$a['y'] = 1;
+		}
+		assertType("array{0: 'z', y?: 1}", $a);
+		assertType('bool', array_is_list($a));
+
+		// Two pure lists merge into a list (optional keys stay a suffix).
+		$b = [0 => 'z'];
+		if (rand(0, 1)) {
+			$b[1] = 'w';
+		}
+		assertType("array{0: 'z', 1?: 'w'}", $b);
+		assertType('true', array_is_list($b));
+
+		// Shapes disjoint except for the empty array still admit the empty list.
+		$c = [];
+		if (rand(0, 1)) {
+			$c['a'] = 1;
+		}
+		assertType('array{}|array{a: 1}', $c);
+		assertType('bool', array_is_list($c));
+	}
+
+}
diff --git a/tests/PHPStan/Type/Constant/ConstantArrayTypeTest.php b/tests/PHPStan/Type/Constant/ConstantArrayTypeTest.php
index 5c85f86026..6e78df2e6d 100644
--- a/tests/PHPStan/Type/Constant/ConstantArrayTypeTest.php
+++ b/tests/PHPStan/Type/Constant/ConstantArrayTypeTest.php
@@ -1639,6 +1639,77 @@ public function testSealedness(): void
 		});
 	}
 
+	/**
+	 * @param list<array{int|string, Type, bool}> $items
+	 */
+	private function buildShape(array $items): ConstantArrayType
+	{
+		$builder = ConstantArrayTypeBuilder::createEmpty();
+		foreach ($items as [$key, $valueType, $optional]) {
+			$keyType = is_string($key) ? new ConstantStringType($key) : new ConstantIntegerType($key);
+			$builder->setOffsetValueType($keyType, $valueType, $optional);
+		}
+		$array = $builder->getArray();
+		$this->assertInstanceOf(ConstantArrayType::class, $array);
+
+		return $array;
+	}
+
+	public function testMakeListProjectsSealedShapeButKeepsUnsealedKeys(): void
+	{
+		// A sealed shape with an optional key past the gap at 1 (2? here): key 2 can
+		// never appear in a list, so makeList() drops it and projects to the prefix.
+		BleedingEdgeToggle::withBleedingEdge(true, function (): void {
+			$array = $this->buildShape([[0, new IntegerType(), false], [2, new StringType(), true]]);
+			$this->assertSame(TrinaryLogic::createMaybe()->describe(), $array->isList()->describe());
+			$this->assertSame('array{int}', $array->makeList()->describe(VerbosityLevel::precise()));
+		});
+
+		// Unsealed: extras may fill the gap, so key 2 is reachable and every key is kept.
+		BleedingEdgeToggle::withBleedingEdge(false, function (): void {
+			$array = $this->buildShape([[0, new IntegerType(), false], [2, new StringType(), true]]);
+			$this->assertSame(TrinaryLogic::createMaybe()->describe(), $array->isList()->describe());
+			$this->assertSame('array{0: int, 2?: string}', $array->makeList()->describe(VerbosityLevel::precise()));
+		});
+	}
+
+	public function testMergeWithRecomputesListnessOfSealedShape(): void
+	{
+		// main mergeWith() path (bleeding edge: shapes carry real unsealed markers)
+		BleedingEdgeToggle::withBleedingEdge(true, function (): void {
+			// Two pure lists merge into a list, even though the merged shape read with
+			// independent optional keys would over-approximate to maybe.
+			$x = $this->buildShape([[0, new IntegerType(), false], [1, new StringType(), true]]);
+			$y = $this->buildShape([[0, new IntegerType(), false], [1, new StringType(), false], [2, new IntegerType(), true]]);
+			$this->assertSame(TrinaryLogic::createYes()->describe(), $x->mergeWith($y)->isList()->describe());
+
+			// A mandatory non-list key that becomes optional through merging turns the
+			// naive `no` into `maybe` (the merged shape now admits list realizations).
+			$x2 = $this->buildShape([[0, new IntegerType(), false], ['a', new StringType(), false]]);
+			$y2 = $this->buildShape([[0, new IntegerType(), false]]);
+			$this->assertSame(TrinaryLogic::createMaybe()->describe(), $x2->mergeWith($y2)->isList()->describe());
+		});
+
+		// legacyMergeWith() path (unsealed === null)
+		BleedingEdgeToggle::withBleedingEdge(false, function (): void {
+			$x = $this->buildShape([[0, new IntegerType(), false], [1, new StringType(), false], [2, new StringType(), false]]);
+			$y = $this->buildShape([[0, new IntegerType(), false]]);
+			$this->assertSame(TrinaryLogic::createYes()->describe(), $x->mergeWith($y)->isList()->describe());
+
+			$x2 = $this->buildShape([[0, new IntegerType(), false], ['a', new StringType(), false]]);
+			$y2 = $this->buildShape([[0, new IntegerType(), false]]);
+			$this->assertSame(TrinaryLogic::createMaybe()->describe(), $x2->mergeWith($y2)->isList()->describe());
+
+			// Legacy merge keeps only $this's keys, so a naive `maybe` (the other side
+			// has a gap key) sharpens back to `yes`: the surviving keys form a list once
+			// the key absent from the other side is widened to a trailing optional.
+			$x3 = $this->buildShape([[0, new IntegerType(), false], [1, new StringType(), false]]);
+			$y3 = $this->buildShape([[0, new IntegerType(), false], [5, new StringType(), true]]);
+			$this->assertSame(TrinaryLogic::createMaybe()->describe(), $y3->isList()->describe());
+			$this->assertSame(TrinaryLogic::createYes()->describe(), $x3->mergeWith($y3)->isList()->describe());
+		});
+	}
+
 	public static function dataGetArraySize(): iterable
 	{
 		$cases = [];