diff --git a/src/rulesets/LinearAlgebra/norm.jl b/src/rulesets/LinearAlgebra/norm.jl
index abd422387..be9ca1ac7 100644
--- a/src/rulesets/LinearAlgebra/norm.jl
+++ b/src/rulesets/LinearAlgebra/norm.jl
@@ -20,28 +20,36 @@ end
 function rrule(::typeof(norm), x::AbstractArray{<:Number}, p::Real)
     y = LinearAlgebra.norm(x, p)
     function norm_pullback_p(Δy)
-        ∂x = if isempty(x) || p == 0
-                InplaceableThunk(
-                    @thunk(zero.(x) .* (zero(y) * zero(real(Δy)))),
-                    identity,
-                )
+        ∂x = InplaceableThunk(
+            # out-of-place versions
+            if isempty(x) || p == 0
+                @thunk(zero.(x) .* (zero(y) * zero(real(Δy))))
             elseif p == 2
-                InplaceableThunk(
-                    @thunk(_norm2_back(x, y, Δy)),
-                    dx -> _norm2_back!(dx, x, y, Δy),
-                )
+                @thunk(_norm2_back(x, y, Δy))
             elseif p == 1
-                InplaceableThunk(
-                    @thunk(_norm1_back(x, y, Δy)),
-                    dx -> _norm1_back!(dx, x, y, Δy),
-                )
+                @thunk(_norm1_back(x, y, Δy))
             elseif p == Inf
-                _normInf_back(x, y, Δy)
+                @thunk(_normInf_back(x, y, Δy))
             elseif p == -Inf
-                _normInf_back(x, y, Δy)
+                @thunk(_normInf_back(x, y, Δy))
             else
-                _normp_back_x(x, p, y, Δy)
+                @thunk(_normp_back_x(x, p, y, Δy))
+            end,
+            # in-place versions
+            if isempty(x) || p == 0
+                identity
+            elseif p == 2
+                dx -> _norm2_back!(dx, x, y, Δy)
+            elseif p == 1
+                dx -> _norm1_back!(dx, x, y, Δy)
+            elseif p == Inf
+                dx -> dx .+= _normInf_back(x, y, Δy)  # not really in-place! could perhaps be improved
+            elseif p == -Inf
+                dx -> dx .+= _normInf_back(x, y, Δy)
+            else
+                dx -> dx .+= _normp_back_x(x, p, y, Δy)
             end
+            )
         ∂p = @thunk _normp_back_p(x, p, y, Δy)
         return (NO_FIELDS, ∂x, ∂p)
     end
@@ -51,14 +59,19 @@ end
 function rrule(::typeof(norm), x::AbstractArray{<:Number})
     y = LinearAlgebra.norm(x)
     function norm_pullback_2(Δy)
-        ∂x = if isempty(x)
-            zero.(x) .* (zero(y) * zero(real(Δy)))
-        else
-            InplaceableThunk(
-                @thunk(_norm2_back(x, y, Δy)),
-                dx -> _norm2_back!(dx, x, y, Δy),
+        ∂x = InplaceableThunk(
+            if isempty(x)
+                @thunk(zero.(x) .* (zero(y) * zero(real(Δy))))
+            else
+                @thunk(_norm2_back(x, y, Δy))
+            end
+            ,
+            if isempty(x)
+                identity
+            else
+                dx -> _norm2_back!(dx, x, y, Δy)
+            end
             )
-        end
         return (NO_FIELDS, ∂x)
     end
     norm_pullback_2(::Zero) = (NO_FIELDS, Zero())