diff --git a/src/Operators/banded/Conversion.jl b/src/Operators/banded/Conversion.jl
index 2a4e61e0..dad79956 100644
--- a/src/Operators/banded/Conversion.jl
+++ b/src/Operators/banded/Conversion.jl
@@ -27,8 +27,10 @@ end
 domainspace(C::ConcreteConversion)=C.domainspace
 rangespace(C::ConcreteConversion)=C.rangespace
 
-promotedomainspace(C::Conversion, sp::Space) = Conversion(sp, rangespace(C))
-promoterangespace(C::Conversion, sp::Space) = Conversion(domainspace(C), sp)
+promotedomainspace(C::Conversion, sp::Space) =
+    sp == domainspace(C) ? C : Conversion(sp, rangespace(C))
+promoterangespace(C::Conversion, sp::Space) =
+    sp == rangespace(C) ? C : Conversion(domainspace(C), sp)
 
 function _implementconversionerror(a, b)
     error("Implement Conversion from ", typeof(a), " to ", typeof(b))
diff --git a/src/Operators/general/algebra.jl b/src/Operators/general/algebra.jl
index 258d14c2..586432bd 100644
--- a/src/Operators/general/algebra.jl
+++ b/src/Operators/general/algebra.jl
@@ -73,10 +73,21 @@ end
 function promoteplus(opsin, sz=size(first(opsin)))
     ops = filter(!iszeroop, opsin)
     ET = promote_eltypeof(opsin)
+    O = eltype(convert_vector(_convertops(Operator{ET}, ops)))
     v = promotespaces(ops)
-    PlusOperator{ET}(convert_vector(v), bandwidthsmax(v), sz,
-        bandwidthsmax(v, blockbandwidths), bandwidthsmax(v, subblockbandwidths))
+    w = convert_vector(v)
+    # The types of the promoted operators may depend on the values of the spaces.
+    # We retain the concrete type if the promotion preserves it (e.g. if the spaces agree),
+    # and store the operators as Operator{ET} otherwise. This limits the result to a small Union
+    if w isa Vector{O}
+        _promoteplus(ET, w, v, sz)
+    else
+        _promoteplus(ET, strictconvert(Vector{Operator{ET}}, w), v, sz)
+    end
 end
+# the bandwidths are computed from v, which may be better inferred than ops
+_promoteplus(::Type{ET}, ops, v, sz) where {ET} = PlusOperator{ET}(ops, bandwidthsmax(v), sz,
+    bandwidthsmax(v, blockbandwidths), bandwidthsmax(v, subblockbandwidths))
 
 domain(P::PlusOperator) = commondomain(P.ops)