diff --git a/Project.toml b/Project.toml
index 18f0776..cc71dee 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "TemporalGPs"
 uuid = "e155a3c4-0841-43e1-8b83-a0e4f03cc18f"
 authors = ["willtebbutt <wt0881@my.bristol.ac.uk> and contributors"]
-version = "0.6.3"
+version = "0.6.4"
 
 [deps]
 AbstractGPs = "99985d1d-32ba-4be9-9821-2ec096f28918"
diff --git a/src/util/chainrules.jl b/src/util/chainrules.jl
index 0d2bec6..9b40b25 100644
--- a/src/util/chainrules.jl
+++ b/src/util/chainrules.jl
@@ -181,15 +181,20 @@ function ChainRulesCore.rrule(config::RuleConfig{>:HasReverseMode}, ::typeof(_ma
     return Fill(y_el, axes(x)), _map_Fill_rrule
 end
 
-function ChainRulesCore.rrule(config::RuleConfig{>:HasReverseMode}, ::typeof(_map), f, x::Fill, y::Fill)
-    z_el, back = ChainRulesCore.rrule_via_ad(config, f, x.value, y.value)
+# Somehow needed to avoid the _map -> map indirection
+function _map(f, xs::Fill...)
+    all(==(axes(first(xs))), axes.(xs)) || error("All axes should be the same")
+    Fill(f(FillArrays.getindex_value.(xs)...), axes(first(xs)))
+end
+
+function ChainRulesCore.rrule(config::RuleConfig{>:HasReverseMode}, ::typeof(_map), f, xs::Fill...)
+    z_el, back = ChainRulesCore.rrule_via_ad(config, f, FillArrays.getindex_value.(xs)...)
     function _map_Fill_rrule(Δ)
-        Δf, Δx_el, Δy_el = back(unthunk(Δ).value)
-        return NoTangent(), Δf, Fill(Δx_el, axes(x)), Fill(Δy_el, axes(x))
+        Δf, Δxs_el... = back(unthunk(Δ).value)
+        return NoTangent(), Δf, Fill.(Δxs_el, axes.(xs))...
     end
-    return Fill(z_el, axes(x)), _map_Fill_rrule
+    return Fill(z_el, axes(first(xs))), _map_Fill_rrule
 end
-
 ### Same thing for `StructArray`
 
 
diff --git a/test/util/chainrules.jl b/test/util/chainrules.jl
index 2fd8267..0d71611 100644
--- a/test/util/chainrules.jl
+++ b/test/util/chainrules.jl
@@ -80,13 +80,17 @@ include("../test_util.jl")
         test_rrule(_map, x -> 2.0 * x, x; check_inferred=false)
         test_rrule(ZygoteRuleConfig(), (x,a)-> _map(x -> x * a, x), x, 2.0; check_inferred=false, rrule_f=rrule_via_ad)
     end
-    @testset "_map(f, x1::Fill, x2::Fill)" begin
+    @testset "_map(f, x::Fill....)" begin
         x1 = Fill(randn(3, 4), 3)
         x2 = Fill(randn(3, 4), 3)
+        x3 = Fill(randn(3, 4), 3)
 
         @test _map(+, x1, x2) == _map(+, collect(x1), collect(x2))
         test_rrule(_map, +, x1, x2; check_inferred=true)
 
+        @test _map(+, x1, x2, x3) == _map(+, collect(x1), collect(x2), collect(x3))
+        test_rrule(_map, +, x1, x2, x3; check_inferred=true)
+
         fsin(x, y) = sin.(x .* y)
         test_rrule(_map, fsin, x1, x2; check_inferred=false)