diff --git a/src/higherorderfns.jl b/src/higherorderfns.jl
index 3a45d195..c79a6123 100644
--- a/src/higherorderfns.jl
+++ b/src/higherorderfns.jl
@@ -973,35 +973,39 @@ broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf,T} = broadcast(x -> f(
 # and rebroadcast. otherwise, divert to generic AbstractArray broadcast code.
 
 struct PromoteToSparse <: Broadcast.AbstractArrayStyle{2} end
-const StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
-Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
-
 PromoteToSparse(::Val{0}) = PromoteToSparse()
 PromoteToSparse(::Val{1}) = PromoteToSparse()
 PromoteToSparse(::Val{2}) = PromoteToSparse()
 PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
 
-Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
-Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
-
-# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
-# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::Type{<:Adjoint{T,<:Vector} where T}) = Broadcast.MatrixStyle() # Adjoint not yet defined when broadcast.jl loaded
-Broadcast.BroadcastStyle(::Type{<:Transpose{T,<:Vector} where T}) = Broadcast.MatrixStyle() # Transpose not yet defined when broadcast.jl loaded
+const StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
+Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
 Broadcast.BroadcastStyle(::Type{<:Adjoint{T,<:Union{SparseVector,SparseMatrixCSC}} where T}) = PromoteToSparse()
 Broadcast.BroadcastStyle(::Type{<:Transpose{T,<:Union{SparseVector,SparseMatrixCSC}} where T}) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
-Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(1)))
-Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.DefaultArrayStyle{N}) where N =
-    Broadcast.DefaultArrayStyle(Broadcast._max(Val(N), Val(2)))
-# end FIXME
 
-broadcast(f, ::PromoteToSparse, ::Nothing, ::Nothing, As::Vararg{Any,N}) where {N} =
-    broadcast(f, map(_sparsifystructured, As)...)
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
+Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
+Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
+
+# FIXME: currently sparse broadcasts are only well-tested on known array types, while any AbstractArray
+# could report itself as a DefaultArrayStyle().
+# See https://github.com/JuliaLang/julia/pull/23939#pullrequestreview-72075382 for more details
+is_supported_sparse_broadcast() = true
+is_supported_sparse_broadcast(::AbstractArray, rest...) = false
+is_supported_sparse_broadcast(::AbstractSparseArray, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(::StructuredMatrix, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(::Array, rest...) = is_supported_sparse_broadcast(rest...)
+is_supported_sparse_broadcast(t::Union{Transpose, Adjoint}, rest...) = is_supported_sparse_broadcast(t.parent, rest...)
+is_supported_sparse_broadcast(x, rest...) = BroadcastStyle(typeof(x)) === Broadcast.Scalar() && is_supported_sparse_broadcast(rest...)
+function broadcast(f, s::PromoteToSparse, ::Nothing, ::Nothing, As::Vararg{Any,N}) where {N}
+    if is_supported_sparse_broadcast(As...)
+        return broadcast(f, map(_sparsifystructured, As)...)
+    else
+        return broadcast(f, Broadcast.ArrayConflict(), nothing, nothing, As...)
+    end
+end
 
 # For broadcast! with ::Any inputs, we need a layer of indirection to determine whether
 # the inputs can be promoted to SparseVecOrMat. If it's just SparseVecOrMat and scalars,