diff --git a/Project.toml b/Project.toml
index 9767e53..0a4bd75 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "LazyArrays"
 uuid = "5078a376-72f3-5289-bfd5-ec5146d43c02"
-version = "2.1.9"
+version = "2.2"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
diff --git a/ext/LazyArraysBandedMatricesExt.jl b/ext/LazyArraysBandedMatricesExt.jl
index dc1ff8b..e596b2c 100644
--- a/ext/LazyArraysBandedMatricesExt.jl
+++ b/ext/LazyArraysBandedMatricesExt.jl
@@ -567,8 +567,8 @@ copy(M::Mul{<:DiagonalLayout, <:BandedLazyLayouts}) = simplify(M)
 copy(M::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}}, <:BandedLazyLayouts}) = copy(mulreduce(M))
 copy(M::Mul{<:BandedLazyLayouts, <:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = copy(mulreduce(M))
 
-simplifiable(::Mul{<:BandedLazyLayouts, <:DiagonalLayout{<:OnesLayout}}) = Val(true)
-simplifiable(::Mul{<:DiagonalLayout{<:OnesLayout}, <:BandedLazyLayouts}) = Val(true)
+simplifiable(::Mul{<:BandedLayouts, <:DiagonalLayout{<:OnesLayout}}) = Val(true)
+simplifiable(::Mul{<:DiagonalLayout{<:OnesLayout}, <:BandedLayouts}) = Val(true)
 copy(M::Mul{<:BandedLazyLayouts, <:DiagonalLayout{<:OnesLayout}}) = _copy_oftype(M.A, eltype(M))
 copy(M::Mul{<:DiagonalLayout{<:OnesLayout}, <:BandedLazyLayouts}) = _copy_oftype(M.B, eltype(M))
 
@@ -644,8 +644,8 @@ copy(M::Mul{<:Union{AbstractStridedLayout,DualLayout{<:AbstractStridedLayout}},
 simplifiable(M::Mul{<:AbstractInvLayout{<:BandedLayouts}, <:Union{PaddedColumns,PaddedLayout,AbstractStridedLayout}}) = Val(true)
 simplifiable(M::Mul{<:Union{PaddedRows,PaddedLayout,DualLayout{<:PaddedRows}}, <:BandedLayouts}) = Val(true)
 simplifiable(M::Mul{<:BandedLayouts, <:Union{PaddedColumns,PaddedLayout}}) = Val(true)
-simplifiable(M::Mul{<:Union{AbstractStridedLayout,DualLayout{<:AbstractStridedLayout}}, <:BandedLazyLayouts}) = Val(true)
-simplifiable(M::Mul{<:BandedLazyLayouts, <:AbstractStridedLayout}) = Val(true)
+simplifiable(M::Mul{<:Union{AbstractStridedLayout,DualLayout{<:AbstractStridedLayout}}, <:BandedLayouts}) = Val(true)
+simplifiable(M::Mul{<:BandedLayouts, <:AbstractStridedLayout}) = Val(true)
 
 copy(L::Ldiv{ApplyBandedLayout{typeof(*)}, Lay}) where Lay = copy(Ldiv{ApplyLayout{typeof(*)},Lay}(L.A, L.B))
 copy(L::Ldiv{ApplyBandedLayout{typeof(*)}, Lay}) where {Lay<:AbstractLazyLayout} = copy(Ldiv{ApplyLayout{typeof(*)},Lay}(L.A, L.B))
diff --git a/src/LazyArrays.jl b/src/LazyArrays.jl
index fb6fe84..008a627 100644
--- a/src/LazyArrays.jl
+++ b/src/LazyArrays.jl
@@ -38,7 +38,7 @@ import ArrayLayouts: AbstractQLayout, Dot, Dotu, Ldiv, Lmul, MatMulMatAdd, MatMu
                      hermitianlayout, layout_getindex, layout_replace_in_print_matrix, ldivaxes, materialize,
                      materialize!, mulreduce, reshapedlayout, rowsupport, scalarone, scalarzero, sub_materialize,
                      sublayout, symmetriclayout, symtridiagonallayout, transposelayout, triangulardata,
-                     triangularlayout, tridiagonallayout, zero!, transtype
+                     triangularlayout, tridiagonallayout, zero!, transtype, OnesLayout
 
 import FillArrays: AbstractFill, getindex_value
 
diff --git a/src/linalg/mul.jl b/src/linalg/mul.jl
index 1cb944b..39afb86 100644
--- a/src/linalg/mul.jl
+++ b/src/linalg/mul.jl
@@ -371,18 +371,23 @@ applylayout(::Type{typeof(*)}, ::DualLayout{Lay}, args...) where Lay = DualLayou
 transtype(A::MulMatrix) = transtype(first(A.args))
 
 #TODO: Why not all DiagonalLayout?
-@inline simplifiable(M::Mul{<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
-@inline simplifiable(M::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
-@inline simplifiable(M::Mul{<:Any,<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:OnesLayout},<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:DiagonalLayout{<:OnesLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:OnesLayout}, <:DiagonalLayout{<:OnesLayout}}) = Val(true) # ambiguity
+@inline simplifiable(::Mul{<:Any,<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:Union{AbstractStridedLayout,DualLayout{<:AbstractStridedLayout}}, <:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:AbstractFillLayout}, <:AbstractStridedLayout}) = Val(true)
 @inline copy(M::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:LazyLayouts}) = copy(mulreduce(M))
 @inline copy(M::Mul{<:LazyLayouts,<:DiagonalLayout{<:AbstractFillLayout}}) = copy(mulreduce(M))
 @inline copy(M::Mul{BroadcastLayout{typeof(*)},<:DiagonalLayout{<:AbstractFillLayout}}) = copy(mulreduce(M))
 
-@inline simplifiable(M::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}},<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
-@inline simplifiable(M::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
-@inline simplifiable(M::Mul{<:Any,<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
-@inline simplifiable(M::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}},<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
-@inline simplifiable(M::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
+@inline simplifiable(::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}},<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
+@inline simplifiable(::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
+@inline simplifiable(::Mul{<:Any,<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
+@inline simplifiable(::Mul{<:Union{ZerosLayout,DualLayout{ZerosLayout}},<:DiagonalLayout{<:AbstractFillLayout}}) = Val(true)
+@inline simplifiable(::Mul{<:DiagonalLayout{<:AbstractFillLayout},<:Union{ZerosLayout,DualLayout{ZerosLayout}}}) = Val(true)
 
 
 # inv
diff --git a/test/multests.jl b/test/multests.jl
index cddfc3f..1735ada 100644
--- a/test/multests.jl
+++ b/test/multests.jl
@@ -1,4 +1,6 @@
-using Test, LinearAlgebra, LazyArrays, StaticArrays, FillArrays, Base64, Random, BandedMatrices
+using Test, LinearAlgebra, LazyArrays, FillArrays, Base64, Random
+using BandedMatrices
+using StaticArrays
 import LazyArrays: MulAdd, MemoryLayout, DenseColumnMajor, DiagonalLayout, SymTridiagonalLayout, Add, AddArray,
                     MulStyle, MulAddStyle, Applied, ApplyStyle, Lmul, ApplyArrayBroadcastStyle, DefaultArrayApplyStyle,
                     Rmul, ApplyLayout, arguments, colsupport, rowsupport, lazymaterialize
@@ -1176,8 +1178,23 @@ end
 
     @testset "simplifiable tests" begin
         A = randn(5,5)
+        b = randn(5)
+        D = Diagonal(Fill(2,5))
+        E = Eye(5)
         @test LazyArrays.simplifiable(*, A) == Val(false)
         @test LazyArrays.simplify(Applied(*, A, A)) == A*A
+        @test LazyArrays.simplifiable(*, A, D) == Val(true)
+        @test LazyArrays.simplifiable(*, D, A) == Val(true)
+        @test LazyArrays.simplifiable(*, b', D) == Val(true)
+        @test LazyArrays.simplifiable(*, D, b) == Val(true)
+        @test LazyArrays.simplifiable(*, A, E) == Val(true)
+        @test LazyArrays.simplifiable(*, E, A) == Val(true)
+        @test LazyArrays.simplifiable(*, b', E) == Val(true)
+        @test LazyArrays.simplifiable(*, E, b) == Val(true)
+        @test LazyArrays.simplifiable(*, E, D) == Val(true)
+        @test LazyArrays.simplifiable(*, D, E) == Val(true)
+        @test LazyArrays.simplifiable(*, D, D) == Val(true)
+        @test LazyArrays.simplifiable(*, E, E) == Val(true)
     end
 end