diff --git a/src/subtype.c b/src/subtype.c
index a0b7bff4006ce..1086d11d2fe8c 100644
--- a/src/subtype.c
+++ b/src/subtype.c
@@ -2678,31 +2678,22 @@ static void set_bound(jl_value_t **bound, jl_value_t *val, jl_tvar_t *v, jl_sten
 // subtype, treating all vars as existential
 static int subtype_in_env_existential(jl_value_t *x, jl_value_t *y, jl_stenv_t *e)
 {
-    jl_varbinding_t *v = e->vars;
-    int len = 0;
     if (x == jl_bottom_type || y == (jl_value_t*)jl_any_type)
         return 1;
-    while (v != NULL) {
-        len++;
-        v = v->prev;
-    }
-    int8_t *rs = (int8_t*)malloc_s(len);
+    int8_t *rs = (int8_t*)alloca(current_env_length(e));
+    jl_varbinding_t *v = e->vars;
     int n = 0;
-    v = e->vars;
-    while (n < len) {
-        assert(v != NULL);
+    while (v != NULL) {
         rs[n++] = v->right;
         v->right = 1;
         v = v->prev;
     }
     int issub = subtype_in_env(x, y, e);
     n = 0; v = e->vars;
-    while (n < len) {
-        assert(v != NULL);
+    while (v != NULL) {
         v->right = rs[n++];
         v = v->prev;
     }
-    free(rs);
     return issub;
 }
 
@@ -2750,6 +2741,8 @@ static int check_unsat_bound(jl_value_t *t, jl_tvar_t *v, jl_stenv_t *e) JL_NOTS
 }
 
 
+static int intersect_var_ccheck_in_env(jl_value_t *xlb, jl_value_t *xub, jl_value_t *ylb, jl_value_t *yub, jl_stenv_t *e, int flip);
+
 static jl_value_t *intersect_var(jl_tvar_t *b, jl_value_t *a, jl_stenv_t *e, int8_t R, int param)
 {
     jl_varbinding_t *bb = lookup(e, b);
@@ -2761,20 +2754,14 @@ static jl_value_t *intersect_var(jl_tvar_t *b, jl_value_t *a, jl_stenv_t *e, int
         return R ? intersect(a, bb->lb, e, param) : intersect(bb->lb, a, e, param);
     if (!jl_is_type(a) && !jl_is_typevar(a))
         return set_var_to_const(bb, a, e, R);
-    jl_savedenv_t se;
     if (param == 2) {
         jl_value_t *ub = NULL;
         JL_GC_PUSH1(&ub);
         if (!jl_has_free_typevars(a)) {
-            save_env(e, &se, 1);
-            int issub = subtype_in_env_existential(bb->lb, a, e);
-            restore_env(e, &se, 1);
-            if (issub) {
-                issub = subtype_in_env_existential(a, bb->ub, e);
-                restore_env(e, &se, 1);
-            }
-            free_env(&se);
-            if (!issub) {
+            if (R) flip_offset(e);
+            int ccheck = intersect_var_ccheck_in_env(bb->lb, bb->ub, a, a, e, !R);
+            if (R) flip_offset(e);
+            if (!ccheck) {
                 JL_GC_POP();
                 return jl_bottom_type;
             }
@@ -2784,6 +2771,7 @@ static jl_value_t *intersect_var(jl_tvar_t *b, jl_value_t *a, jl_stenv_t *e, int
             e->triangular++;
             ub = R ? intersect_aside(a, bb->ub, e, bb->depth0) : intersect_aside(bb->ub, a, e, bb->depth0);
             e->triangular--;
+            jl_savedenv_t se;
             save_env(e, &se, 1);
             int issub = subtype_in_env_existential(bb->lb, ub, e);
             restore_env(e, &se, 1);
@@ -3856,6 +3844,89 @@ static int subtype_by_bounds(jl_value_t *x, jl_value_t *y, jl_stenv_t *e) JL_NOT
     return compareto_var(x, (jl_tvar_t*)y, e, -1) || compareto_var(y, (jl_tvar_t*)x, e, 1);
 }
 
+static int intersect_var_ccheck_in_env(jl_value_t *xlb, jl_value_t *xub, jl_value_t *ylb, jl_value_t *yub, jl_stenv_t *e, int flip)
+{
+    int easy_check1 = xlb == jl_bottom_type ||
+                      yub == (jl_value_t *)jl_any_type ||
+                      (e->Loffset == 0 && obviously_in_union(yub, xlb));
+    int easy_check2 = ylb == jl_bottom_type ||
+                      xub == (jl_value_t *)jl_any_type ||
+                      (e->Loffset == 0 && obviously_in_union(xub, ylb));
+    int nofree1 = 0, nofree2 = 0;
+    if (!easy_check1) {
+        nofree1 = !jl_has_free_typevars(xlb) && !jl_has_free_typevars(yub);
+        if (nofree1 && e->Loffset == 0) {
+            easy_check1 = jl_subtype(xlb, yub);
+            if (!easy_check1)
+                return 0;
+        }
+    }
+    if (!easy_check2) {
+        nofree2 = !jl_has_free_typevars(ylb) && !jl_has_free_typevars(xub);
+        if (nofree2 && e->Loffset == 0) {
+            easy_check2 = jl_subtype(ylb, xub);
+            if (!easy_check2)
+                return 0;
+        }
+    }
+    if (easy_check1 && easy_check2)
+        return 1;
+    int ccheck = 0;
+    if ((easy_check1 || nofree1) && (easy_check2 || nofree2)) {
+        jl_varbinding_t *vars = e->vars;
+        e->vars = NULL;
+        ccheck = easy_check1 || subtype_in_env(xlb, yub, e);
+        if (ccheck && !easy_check2) {
+            flip_offset(e);
+            ccheck = subtype_in_env(ylb, xub, e);
+            flip_offset(e);
+        }
+        e->vars = vars;
+        return ccheck;
+    }
+    jl_savedenv_t se;
+    save_env(e, &se, 1);
+    // first try normal flip.
+    if (flip) flip_vars(e);
+    ccheck = easy_check1 || subtype_in_env(xlb, yub, e);
+    if (ccheck && !easy_check2) {
+        flip_offset(e);
+        ccheck = subtype_in_env(ylb, xub, e);
+        flip_offset(e);
+    }
+    if (flip) flip_vars(e);
+    if (!ccheck) {
+        // then try reverse flip.
+        restore_env(e, &se, 1);
+        if (!flip) flip_vars(e);
+        ccheck = easy_check1 || subtype_in_env(xlb, yub, e);
+        if (ccheck && !easy_check2) {
+            flip_offset(e);
+            ccheck = subtype_in_env(ylb, xub, e);
+            flip_offset(e);
+        }
+        if (!flip) flip_vars(e);
+    }
+    if (!ccheck) {
+        // then try existential.
+        restore_env(e, &se, 1);
+        if (easy_check1)
+            ccheck = 1;
+        else {
+            ccheck = subtype_in_env_existential(xlb, yub, e);
+            restore_env(e, &se, 1);
+        }
+        if (ccheck && !easy_check2) {
+            flip_offset(e);
+            ccheck = subtype_in_env_existential(ylb, xub, e);
+            flip_offset(e);
+            restore_env(e, &se, 1);
+        }
+    }
+    free_env(&se);
+    return ccheck;
+}
+
 static int has_typevar_via_env(jl_value_t *x, jl_tvar_t *t, jl_stenv_t *e)
 {
     if (e->Loffset == 0) {
@@ -3988,14 +4059,8 @@ static jl_value_t *intersect(jl_value_t *x, jl_value_t *y, jl_stenv_t *e, int pa
                     ccheck = 1;
                 }
                 else {
-                    if (R) flip_vars(e);
-                    ccheck = subtype_in_env(xlb, yub, e);
-                    if (ccheck) {
-                        flip_offset(e);
-                        ccheck = subtype_in_env(ylb, xub, e);
-                        flip_offset(e);
-                    }
-                    if (R) flip_vars(e);
+                    // try many subtype check to avoid false `Union{}`
+                    ccheck = intersect_var_ccheck_in_env(xlb, xub, ylb, yub, e, R);
                 }
                 if (R) flip_offset(e);
                 if (!ccheck)
diff --git a/test/subtype.jl b/test/subtype.jl
index ba7f86bb86a14..979746bd626dc 100644
--- a/test/subtype.jl
+++ b/test/subtype.jl
@@ -1691,9 +1691,7 @@ CovType{T} = Union{AbstractArray{T,2},
 # issue #31703
 @testintersect(Pair{<:Any, Ref{Tuple{Ref{Ref{Tuple{Int}}},Ref{Float64}}}},
                Pair{T, S} where S<:(Ref{A} where A<:(Tuple{C,Ref{T}} where C<:(Ref{D} where D<:(Ref{E} where E<:Tuple{FF}) where FF<:B)) where B) where T,
-               Pair{T, Ref{Tuple{Ref{Ref{Tuple{Int}}},Ref{Float64}}}} where T)
-# TODO: should be able to get this result
-#              Pair{Float64, Ref{Tuple{Ref{Ref{Tuple{Int}}},Ref{Float64}}}}
+               Pair{Float64, Ref{Tuple{Ref{Ref{Tuple{Int}}},Ref{Float64}}}})
 
 module I31703
 using Test, LinearAlgebra
@@ -1745,8 +1743,7 @@ end
                Tuple{Type{SA{2, L}}, Type{SA{2, L}}} where L)
 @testintersect(Tuple{Type{SA{2, L}}, Type{SA{2, 16}}} where L,
                Tuple{Type{<:SA{N, L}}, Type{<:SA{N, L}}} where {N,L},
-               # TODO: this could be narrower
-               Tuple{Type{SA{2, L}}, Type{SA{2, 16}}} where L)
+               Tuple{Type{SA{2, 16}}, Type{SA{2, 16}}})
 
 # issue #31993
 @testintersect(Tuple{Type{<:AbstractVector{T}}, Int} where T,
@@ -1851,9 +1848,9 @@ c32703(::Type{<:Str{C}}, str::Str{C}) where {C<:CSE} = str
                Tuple{Type{<:Str{C}}, Str{C}} where {C<:CSE},
                Union{})
 @test c32703(UTF16Str, ASCIIStr()) == 42
-@test_broken typeintersect(Tuple{Vector{Vector{Float32}},Matrix,Matrix},
-                           Tuple{Vector{V},Matrix{Int},Matrix{S}} where {S, V<:AbstractVector{S}}) ==
-             Tuple{Array{Array{Float32,1},1},Array{Int,2},Array{Float32,2}}
+@testintersect(Tuple{Vector{Vector{Float32}},Matrix,Matrix},
+               Tuple{Vector{V},Matrix{Int},Matrix{S}} where {S, V<:AbstractVector{S}},
+               Tuple{Array{Array{Float32,1},1},Array{Int,2},Array{Float32,2}})
 
 @testintersect(Tuple{Pair{Int, DataType}, Any},
                Tuple{Pair{A, B} where B<:Type, Int} where A,
@@ -2469,6 +2466,11 @@ end
 abstract type P47654{A} end
 @test Wrapper47654{P47654, Vector{Union{P47654,Nothing}}} <: Wrapper47654
 
+#issue 41561
+@testintersect(Tuple{Vector{VT}, Vector{VT}} where {N1, VT<:AbstractVector{N1}},
+               Tuple{Vector{VN} where {N, VN<:AbstractVector{N}}, Vector{Vector{Float64}}},
+               Tuple{Vector{Vector{Float64}}, Vector{Vector{Float64}}})
+
 @testset "known subtype/intersect issue" begin
     #issue 45874
     let S = Pair{Val{P}, AbstractVector{<:Union{P,<:AbstractMatrix{P}}}} where P,
@@ -2476,9 +2478,6 @@ abstract type P47654{A} end
         @test S <: T
     end
 
-    #issue 41561
-    @test_broken typeintersect(Tuple{Vector{VT}, Vector{VT}} where {N1, VT<:AbstractVector{N1}},
-                Tuple{Vector{VN} where {N, VN<:AbstractVector{N}}, Vector{Vector{Float64}}}) !== Union{}
     #issue 40865
     @test Tuple{Set{Ref{Int}}, Set{Ref{Int}}} <: Tuple{Set{KV}, Set{K}} where {K,KV<:Union{K,Ref{K}}}
     @test Tuple{Set{Val{Int}}, Set{Val{Int}}} <: Tuple{Set{KV}, Set{K}} where {K,KV<:Union{K,Val{K}}}
@@ -2746,3 +2745,15 @@ end
     Val{Tuple{T,R,S}} where {T,R<:Vector{T},S<:Vector{R}},
     Val{Tuple{Int, Vector{Int}, T}} where T<:Vector{Vector{Int}},
 )
+
+#issue 57429
+@testintersect(
+    Pair{<:Any, <:Tuple{Int}},
+    Pair{N, S} where {N, NTuple{N,Int}<:S<:NTuple{M,Int} where {M}},
+    !Union{}
+)
+@testintersect(
+    Pair{N, T} where {N,NTuple{N,Int}<:T<:NTuple{N,Int}},
+    Pair{N, T} where {N,NTuple{N,Int}<:T<:Tuple{Int,Vararg{Int}}},
+    !Union{}
+)