diff --git a/Project.toml b/Project.toml
index 36edfbd21..403da1e65 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.26.4"
+version = "1.26.5"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/projection.jl b/src/projection.jl
index 90e11ddb4..ca577aef2 100644
--- a/src/projection.jl
+++ b/src/projection.jl
@@ -221,23 +221,9 @@ function ProjectTo(xs::AbstractArray)
     end
 end
 
-function (project::ProjectTo{AbstractArray})(dx::AbstractArray{S,M}) where {S,M}
-    # First deal with shape. The rule is that we reshape to add or remove trivial dimensions
-    # like dx = ones(4,1), where x = ones(4), but throw an error on dx = ones(1,4) etc.
-    dy = if axes(dx) === project.axes
-        dx
-    elseif project.axes isa Tuple{Vararg{Base.OneTo}} && axes(dx) isa typeof(project.axes)
-        # Same number of `OneTo` axes that are not identical: the sizes differ. Resolved from
-        # the types alone, so inference does not see the type-unstable `reshape` below.
-        throw(_projection_mismatch(project.axes, size(dx)))
-    else
-        for d in 1:max(M, length(project.axes))
-            if size(dx, d) != length(get(project.axes, d, 1))
-                throw(_projection_mismatch(project.axes, size(dx)))
-            end
-        end
-        reshape(dx, project.axes)
-    end
+function (project::ProjectTo{AbstractArray})(dx::AbstractArray{S}) where {S}
+    # First deal with shape:
+    dy = _projection_reshape(project.axes, dx)
     # Then deal with the elements. One projector if AbstractArray{<:Number},
     # or one per element for arrays of anything else, including arrays of arrays:
     dz = if hasproperty(project, :element)
@@ -270,6 +256,25 @@ function (project::ProjectTo{AbstractArray})(dx::Number) # ... so we restore fro
     return fill(project.element(dx))
 end
 
+# Reshape dx to axes_x, adding or removing trivial dimensions like dx = ones(4,1),
+# where x = ones(4), but throw an error on dx = ones(1,4) etc.
+function _projection_reshape(axes_x::Tuple, dx::AbstractArray)
+    return if axes(dx) === axes_x
+        dx
+    elseif axes_x isa Tuple{Vararg{Base.OneTo}} && axes(dx) isa typeof(axes_x)
+        # Same number of `OneTo` axes that are not identical: the sizes differ. Resolved from
+        # the types alone, so inference does not see the type-unstable `reshape` below.
+        throw(_projection_mismatch(axes_x, size(dx)))
+    else
+        for d in 1:max(ndims(dx), length(axes_x))
+            if size(dx, d) != length(get(axes_x, d, 1))
+                throw(_projection_mismatch(axes_x, size(dx)))
+            end
+        end
+        reshape(dx, axes_x)
+    end
+end
+
 function _projection_mismatch(axes_x::Tuple, size_dx::Tuple)
     size_x = map(length, axes_x)
     return DimensionMismatch(
@@ -439,7 +444,11 @@ end
 
 # Diagonal
 ProjectTo(x::Diagonal) = ProjectTo{Diagonal}(; diag=ProjectTo(x.diag))
-(project::ProjectTo{Diagonal})(dx::AbstractMatrix) = Diagonal(project.diag(diag(dx)))
+function (project::ProjectTo{Diagonal})(dx::AbstractArray)
+    ax = only(project.diag.axes)
+    dy = _projection_reshape((ax, ax), dx)
+    return Diagonal(project.diag(diag(dy)))
+end
 (project::ProjectTo{Diagonal})(dx::Diagonal) = Diagonal(project.diag(dx.diag))
 
 # Symmetric
@@ -489,10 +498,12 @@ end
 # Weird -- not exhaustive!
 # one strategy is to recurse into the struct:
 ProjectTo(x::Bidiagonal{T}) where {T<:Number} = generic_projector(x)
-function (project::ProjectTo{Bidiagonal})(dx::AbstractMatrix)
+function (project::ProjectTo{Bidiagonal})(dx::AbstractArray)
+    ax = only(project.dv.axes)
+    dy = _projection_reshape((ax, ax), dx)
     uplo = LinearAlgebra.sym_uplo(project.uplo)
-    dv = project.dv(diag(dx))
-    ev = project.ev(uplo === :U ? diag(dx, 1) : diag(dx, -1))
+    dv = project.dv(diag(dy))
+    ev = project.ev(uplo === :U ? diag(dy, 1) : diag(dy, -1))
     return Bidiagonal(dv, ev, uplo)
 end
 function (project::ProjectTo{Bidiagonal})(dx::Bidiagonal)
@@ -507,9 +518,11 @@ function (project::ProjectTo{Bidiagonal})(dx::Bidiagonal)
 end
 
 ProjectTo(x::SymTridiagonal{T}) where {T<:Number} = generic_projector(x)
-function (project::ProjectTo{SymTridiagonal})(dx::AbstractMatrix)
-    dv = project.dv(diag(dx))
-    ev = project.ev((diag(dx, 1) .+ diag(dx, -1)) ./ 2)
+function (project::ProjectTo{SymTridiagonal})(dx::AbstractArray)
+    ax = only(project.dv.axes)
+    dy = _projection_reshape((ax, ax), dx)
+    dv = project.dv(diag(dy))
+    ev = project.ev((diag(dy, 1) .+ diag(dy, -1)) ./ 2)
     return SymTridiagonal(dv, ev)
 end
 (project::ProjectTo{SymTridiagonal})(dx::SymTridiagonal) = generic_projection(project, dx)
diff --git a/test/projection.jl b/test/projection.jl
index 912131242..95046147a 100644
--- a/test/projection.jl
+++ b/test/projection.jl
@@ -322,6 +322,18 @@ struct NoSuperType end
         @test pstri(stri) == real(stri)
         @test_throws DimensionMismatch pstri(rand(ComplexF32, 3, 2))
 
+        # same shape rules as ProjectTo{AbstractArray}, e.g. trailing singleton dimensions
+        for p in (pdiag, pbi, pstri)
+            @test @inferred(p(reshape(1:9, 3, 3, 1))) == p(reshape(1:9, 3, 3))
+            @test p(reshape(1:9, 3, 3, 1, 1)) == p(reshape(1:9, 3, 3))
+            @test p(rand(ComplexF32, 3, 3, 1)) isa typeof(p(rand(3, 3)))
+            @test_throws DimensionMismatch p(rand(3, 3, 2))
+            @test_throws DimensionMismatch p(rand(3, 1, 3))
+            @test_throws DimensionMismatch p(rand(3, 4))
+        end
+        psdiag = ProjectTo(Diagonal(SA[1.0, 2.0, 3.0]))
+        @test psdiag(reshape(1:9, 3, 3, 1)) == psdiag(reshape(1:9, 3, 3))
+
         ptri = ProjectTo(Tridiagonal(rand(3, 3)))
         @test ptri(reshape(1:9, 3, 3)) == [1.0 4.0 0.0; 2.0 5.0 8.0; 0.0 6.0 9.0]
         @test ptri(ptri(reshape(1:9, 3, 3))) == ptri(reshape(1:9, 3, 3))