diff --git a/base/compiler/typelimits.jl b/base/compiler/typelimits.jl
index 074e3f91f3d58..15268f3363bb1 100644
--- a/base/compiler/typelimits.jl
+++ b/base/compiler/typelimits.jl
@@ -39,6 +39,8 @@ function is_derived_type(@nospecialize(t), @nospecialize(c), mindepth::Int)
     if t === c
         return mindepth <= 1
     end
+    isvarargtype(t) && (t = unwrapva(t))
+    isvarargtype(c) && (c = unwrapva(c))
     if isa(c, Union)
         # see if it is one of the elements of the union
         return is_derived_type(t, c.a, mindepth) || is_derived_type(t, c.b, mindepth)
@@ -46,8 +48,6 @@ function is_derived_type(@nospecialize(t), @nospecialize(c), mindepth::Int)
         # see if it is derived from the body
         # also handle the var here, since this construct bounds the mindepth to the smallest possible value
         return is_derived_type(t, c.var.ub, mindepth) || is_derived_type(t, c.body, mindepth)
-    elseif isvarargtype(c)
-        return is_derived_type(t, unwrapva(c), mindepth)
     elseif isa(c, DataType)
         if mindepth > 0
             mindepth -= 1
@@ -114,10 +114,14 @@ function _limit_type_size(@nospecialize(t), @nospecialize(c), sources::SimpleVec
             return Union{a, b}
         end
     elseif isa(t, DataType)
-        if isType(t) # allow taking typeof as Type{...}, but ensure it doesn't start nesting
+        if isType(t) # see equivalent case in type_more_complex
             tt = unwrap_unionall(t.parameters[1])
-            (!isa(tt, DataType) || isType(tt)) && (depth += 1)
-            is_derived_type_from_any(tt, sources, depth) && return t
+            if isa(tt, Union) || isa(tt, TypeVar) || isType(tt)
+                is_derived_type_from_any(tt, sources, depth + 1) && return t
+            else
+                isType(c) && (c = unwrap_unionall(c.parameters[1]))
+                type_more_complex(tt, c, sources, depth, 0, 0) || return t
+            end
             return Type
         elseif isa(c, DataType)
             tP = t.parameters
@@ -167,6 +171,11 @@ end
 
 # helper function of `_limit_type_size`, which has the right to take and return `TypeVar` / `Vararg`
 function __limit_type_size(@nospecialize(t), @nospecialize(c), sources::SimpleVector, depth::Int, allowed_tuplelen::Int)
+    cN = 0
+    if isvarargtype(c) # Tuple{Vararg{T}} --> Tuple{T} is OK
+        isdefined(c, :N) && (cN = c.N)
+        c = unwrapva(c)
+    end
     if isa(c, TypeVar)
         if isa(t, TypeVar) && t.ub === c.ub && (t.lb === Union{} || t.lb === c.lb)
             return t # it's ok to change the name, or widen `lb` to Union{}, so we can handle this immediately here
@@ -176,15 +185,17 @@ function __limit_type_size(@nospecialize(t), @nospecialize(c), sources::SimpleVe
         # don't have a matching TypeVar in comparison, so we keep just the upper bound
         return __limit_type_size(t.ub, c, sources, depth, allowed_tuplelen)
     elseif isvarargtype(t)
-        isvarargtype(c) || return Vararg
-        VaT = __limit_type_size(unwrapva(t), unwrapva(c), sources, depth + 1, 0)
-        if isdefined(t, :N) && (isa(t.N, TypeVar) || (isdefined(c, :N) && t.N === c.N))
-            return Vararg{VaT, t.N}
+        # Tuple{Vararg{T,N}} --> Tuple{Vararg{S,M}} is OK
+        # Tuple{T} --> Tuple{Vararg{T}} is OK
+        # but S must be more limited than T, and must not introduce a new number for M
+        VaT = __limit_type_size(unwrapva(t), c, sources, depth + 1, 0)
+        if isdefined(t, :N)
+            tN = t.N
+            if isa(tN, TypeVar) || tN === cN
+                return Vararg{VaT, tN}
+            end
         end
         return Vararg{VaT}
-    elseif isvarargtype(c)
-        # Tuple{Vararg{T}} --> Tuple{T} is OK
-        return __limit_type_size(t, unwrapva(c), sources, depth, 0)
     else
         return _limit_type_size(t, c, sources, depth, allowed_tuplelen)
     end
@@ -205,6 +216,8 @@ function type_more_complex(@nospecialize(t), @nospecialize(c), sources::SimpleVe
         return false # t isn't something new
     end
     # peel off wrappers
+    isvarargtype(t) && (t = unwrapva(t))
+    isvarargtype(c) && (c = unwrapva(c))
     if isa(c, UnionAll)
         # allow wrapping type with fewer UnionAlls than comparison if in a covariant context
         if !isa(t, UnionAll) && tupledepth == 0
@@ -233,18 +246,19 @@ function type_more_complex(@nospecialize(t), @nospecialize(c), sources::SimpleVe
         return t !== 1 && !(0 <= t < c) # alternatively, could use !(abs(t) <= abs(c) || abs(t) < n) for some n
     end
     # base case for data types
-    if isvarargtype(t)
-        if isvarargtype(c)
-            return type_more_complex(unwrapva(t), unwrapva(c), sources, depth + 1, tupledepth, 0)
-        end
-    elseif isa(t, DataType)
+    if isa(t, DataType)
         tP = t.parameters
-        if isvarargtype(c)
-            return type_more_complex(t, unwrapva(c), sources, depth, tupledepth, 0)
-        elseif isType(t) # allow taking typeof any source type anywhere as Type{...}, as long as it isn't nesting Type{Type{...}}
+        if isType(t)
+            # Treat Type{T} and T as equivalent to allow taking typeof any
+            # source type (DataType) anywhere as Type{...}, as long as it isn't
+            # nesting as Type{Type{...}}
             tt = unwrap_unionall(t.parameters[1])
-            (!isa(tt, DataType) || isType(tt)) && (depth += 1)
-            return !is_derived_type_from_any(tt, sources, depth)
+            if isa(tt, Union) || isa(tt, TypeVar) || isType(tt)
+                return !is_derived_type_from_any(tt, sources, depth + 1)
+            else
+                isType(c) && (c = unwrap_unionall(c.parameters[1]))
+                return type_more_complex(tt, c, sources, depth, 0, 0)
+            end
         elseif isa(c, DataType) && t.name === c.name
             cP = c.parameters
             length(cP) < length(tP) && return true
diff --git a/test/compiler/inference.jl b/test/compiler/inference.jl
index 3d9209a1cf49b..7e6a720540a57 100644
--- a/test/compiler/inference.jl
+++ b/test/compiler/inference.jl
@@ -46,8 +46,42 @@ end
 
 # obtain Vararg with 2 undefined fields
 let va = ccall(:jl_type_intersection_with_env, Any, (Any, Any), Tuple{Tuple}, Tuple{Tuple{Vararg{Any, N}}} where N)[2][1]
-    @test Core.Compiler.__limit_type_size(Tuple, va, Core.svec(va, Union{}), 2, 2) === Any
-end
+    @test Core.Compiler.__limit_type_size(Tuple, va, Core.svec(va, Union{}), 2, 2) === Tuple
+end
+
+# issue #42835
+@test !Core.Compiler.type_more_complex(Int, Any, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Int, Type{Int}, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Type{Int}, Any, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Int}}, Type{Int}, Core.svec(Type{Int}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Int}}, Int, Core.svec(Type{Int}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Int}}, Any, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Type{Int}}}, Type{Type{Int}}, Core.svec(Type{Type{Int}}), 1, 1, 1)
+
+@test  Core.Compiler.type_more_complex(ComplexF32, Any, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(ComplexF32, Any, Core.svec(Type{ComplexF32}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(ComplexF32, Type{ComplexF32}, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Type{ComplexF32}, Any, Core.svec(Type{Type{ComplexF32}}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{ComplexF32}, Type{Type{ComplexF32}}, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Type{ComplexF32}, ComplexF32, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{ComplexF32}, Any, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{ComplexF32}}, Type{ComplexF32}, Core.svec(Type{ComplexF32}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{ComplexF32}}, ComplexF32, Core.svec(ComplexF32), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Type{ComplexF32}}}, Type{Type{ComplexF32}}, Core.svec(Type{ComplexF32}), 1, 1, 1)
+
+# n.b. Type{Type{Union{}} === Type{Core.TypeofBottom}
+@test !Core.Compiler.type_more_complex(Type{Union{}}, Any, Core.svec(), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Type{Type{Union{}}}, Any, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Type{Union{}}}}, Any, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Type{Union{}}}}, Type{Type{Union{}}}, Core.svec(Type{Type{Union{}}}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Type{Type{Type{Union{}}}}}, Type{Type{Type{Union{}}}}, Core.svec(Type{Type{Type{Union{}}}}), 1, 1, 1)
+
+@test !Core.Compiler.type_more_complex(Type{1}, Type{2}, Core.svec(), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{Union{Float32,Float64}}, Union{Float32,Float64}, Core.svec(Union{Float32,Float64}), 1, 1, 1)
+@test !Core.Compiler.type_more_complex(Type{Union{Float32,Float64}}, Union{Float32,Float64}, Core.svec(Union{Float32,Float64}), 0, 1, 1)
+@test_broken Core.Compiler.type_more_complex(Type{<:Union{Float32,Float64}}, Type{Union{Float32,Float64}}, Core.svec(Union{Float32,Float64}), 1, 1, 1)
+@test  Core.Compiler.type_more_complex(Type{<:Union{Float32,Float64}}, Any, Core.svec(Union{Float32,Float64}), 1, 1, 1)
+
 
 let # 40336
     t = Type{Type{Int}}