diff --git a/mypy/solve.py b/mypy/solve.py
index 57988790a727..023a32dbd04b 100644
--- a/mypy/solve.py
+++ b/mypy/solve.py
@@ -9,7 +9,7 @@
 from mypy.constraints import SUBTYPE_OF, SUPERTYPE_OF, Constraint, infer_constraints, neg_op
 from mypy.expandtype import expand_type
 from mypy.graph_utils import prepare_sccs, strongly_connected_components, topsort
-from mypy.join import join_types
+from mypy.join import join_type_list
 from mypy.meet import meet_type_list, meet_types
 from mypy.subtypes import is_subtype
 from mypy.typeops import get_all_type_vars
@@ -247,10 +247,16 @@ def solve_iteratively(
     return solutions
 
 
+def _join_sorted_key(t: Type) -> int:
+    t = get_proper_type(t)
+    if isinstance(t, UnionType):
+        return -1
+    return 0
+
+
 def solve_one(lowers: Iterable[Type], uppers: Iterable[Type]) -> Type | None:
     """Solve constraints by finding by using meets of upper bounds, and joins of lower bounds."""
-    bottom: Type | None = None
-    top: Type | None = None
+
     candidate: Type | None = None
 
     # Filter out previous results of failed inference, they will only spoil the current pass...
@@ -267,19 +273,26 @@ def solve_one(lowers: Iterable[Type], uppers: Iterable[Type]) -> Type | None:
         candidate.ambiguous = True
         return candidate
 
+    bottom: Type | None = None
+    top: Type | None = None
+
     # Process each bound separately, and calculate the lower and upper
     # bounds based on constraints. Note that we assume that the constraint
     # targets do not have constraint references.
-    for target in lowers:
-        if bottom is None:
-            bottom = target
-        else:
-            if type_state.infer_unions:
-                # This deviates from the general mypy semantics because
-                # recursive types are union-heavy in 95% of cases.
-                bottom = UnionType.make_union([bottom, target])
-            else:
-                bottom = join_types(bottom, target)
+    if type_state.infer_unions:
+        # This deviates from the general mypy semantics because
+        # recursive types are union-heavy in 95% of cases.
+        bottom = UnionType.make_union(list(lowers))
+    else:
+        # The order of lowers is non-deterministic.
+        # We attempt to sort lowers because joins are non-associative. For instance:
+        # join(join(int, str), int | str) == join(object, int | str) == object
+        # join(int, join(str, int | str)) == join(int, int | str)    == int | str
+        # Note that joins in theory should be commutative, but in practice some bugs mean this is
+        # also a source of non-deterministic type checking results.
+        sorted_lowers = sorted(lowers, key=_join_sorted_key)
+        if sorted_lowers:
+            bottom = join_type_list(sorted_lowers)
 
     for target in uppers:
         if top is None:
diff --git a/test-data/unit/check-generics.test b/test-data/unit/check-generics.test
index 767b55efcac2..35357f8c930f 100644
--- a/test-data/unit/check-generics.test
+++ b/test-data/unit/check-generics.test
@@ -3563,3 +3563,43 @@ def foo(x: T):
     reveal_type(C)  # N: Revealed type is "Overload(def [T, S] (x: builtins.int, y: S`-1) -> __main__.C[__main__.Int[S`-1]], def [T, S] (x: builtins.str, y: S`-1) -> __main__.C[__main__.Str[S`-1]])"
     reveal_type(C(0, x))  # N: Revealed type is "__main__.C[__main__.Int[T`-1]]"
     reveal_type(C("yes", x))  # N: Revealed type is "__main__.C[__main__.Str[T`-1]]"
+
+[case testDeterminismFromJoinOrderingInSolver]
+# Used to fail non-deterministically
+# https://github.com/python/mypy/issues/19121
+from __future__ import annotations
+from typing import Generic, Iterable, Iterator, Self, TypeVar
+
+_T1 = TypeVar("_T1")
+_T2 = TypeVar("_T2")
+_T3 = TypeVar("_T3")
+_T_co = TypeVar("_T_co", covariant=True)
+
+class Base(Iterable[_T1]):
+    def __iter__(self) -> Iterator[_T1]: ...
+class A(Base[_T1]): ...
+class B(Base[_T1]): ...
+class C(Base[_T1]): ...
+class D(Base[_T1]): ...
+class E(Base[_T1]): ...
+
+class zip2(Generic[_T_co]):
+    def __new__(
+        cls,
+        iter1: Iterable[_T1],
+        iter2: Iterable[_T2],
+        iter3: Iterable[_T3],
+    ) -> zip2[tuple[_T1, _T2, _T3]]: ...
+    def __iter__(self) -> Self: ...
+    def __next__(self) -> _T_co: ...
+
+def draw(
+    colors1: A[str] | B[str] | C[int] | D[int | str],
+    colors2: A[str] | B[str] | C[int] | D[int | str],
+    colors3: A[str] | B[str] | C[int] | D[int | str],
+) -> None:
+    for c1, c2, c3 in zip2(colors1, colors2, colors3):
+        reveal_type(c1)  # N: Revealed type is "Union[builtins.int, builtins.str]"
+        reveal_type(c2)  # N: Revealed type is "Union[builtins.int, builtins.str]"
+        reveal_type(c3)  # N: Revealed type is "Union[builtins.int, builtins.str]"
+[builtins fixtures/tuple.pyi]
diff --git a/test-data/unit/check-recursive-types.test b/test-data/unit/check-recursive-types.test
index 00d5489e515a..7f6e181a16ca 100644
--- a/test-data/unit/check-recursive-types.test
+++ b/test-data/unit/check-recursive-types.test
@@ -54,7 +54,7 @@ reveal_type(flatten([1, [2, [3]]]))  # N: Revealed type is "builtins.list[builti
 
 class Bad: ...
 x: Nested[int] = [1, [2, [3]]]
-x = [1, [Bad()]]  # E: List item 0 has incompatible type "Bad"; expected "Union[int, Nested[int]]"
+x = [1, [Bad()]]  # E: List item 1 has incompatible type "List[Bad]"; expected "Union[int, Nested[int]]"
 [builtins fixtures/isinstancelist.pyi]
 
 [case testRecursiveAliasGenericInferenceNested]
@@ -605,7 +605,7 @@ class NT(NamedTuple, Generic[T]):
 class A: ...
 class B(A): ...
 
-nti: NT[int] = NT(key=0, value=NT(key=1, value=A()))  # E: Argument "value" to "NT" has incompatible type "A"; expected "Union[int, NT[int]]"
+nti: NT[int] = NT(key=0, value=NT(key=1, value=A()))  # E: Argument "value" to "NT" has incompatible type "NT[A]"; expected "Union[int, NT[int]]"
 reveal_type(nti)  # N: Revealed type is "Tuple[builtins.int, Union[builtins.int, ...], fallback=__main__.NT[builtins.int]]"
 
 nta: NT[A]