diff --git a/Project.toml b/Project.toml
index 97adf6111..691caead5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Tapir"
 uuid = "07d77754-e150-4737-8c94-cd238a1fb45b"
 authors = ["Will Tebbutt, Hong Ge, and contributors"]
-version = "0.2.3"
+version = "0.2.4"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/interface.jl b/src/interface.jl
index 30f7bbb0c..b40637c5c 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -1,32 +1,33 @@
 """
-    value_and_pullback!!(rule, ȳ, f::CoDual, x::CoDual...)
+    __value_and_pullback!!(rule, ȳ, f::CoDual, x::CoDual...)
 
 In-place version of `value_and_pullback!!` in which the arguments have been wrapped in
 `CoDual`s. Note that any mutable data in `f` and `x` will be incremented in-place. As such,
 if calling this function multiple times with different values of `x`, should be careful to
 ensure that you zero-out the tangent fields of `x` each time.
 """
-function value_and_pullback!!(rule::R, ȳ::T, fx::Vararg{CoDual, N}) where {R, N, T}
-    out, pb!! = rule(fx...)
+function __value_and_pullback!!(rule::R, ȳ::T, fx::Vararg{CoDual, N}) where {R, N, T}
+    out, pb!! = rule(tuple_map(to_fwds, fx)...)
     @assert _typeof(tangent(out)) == fdata_type(T)
     increment!!(tangent(out), fdata(ȳ))
     v = copy(primal(out))
-    return v, pb!!(rdata(ȳ))
+    return v, tuple_map((f, r) -> tangent(fdata(tangent(f)), r), fx, pb!!(rdata(ȳ)))
 end
 
 """
-    value_and_gradient!!(rule, f::CoDual, x::CoDual...)
+    __value_and_gradient!!(rule, f::CoDual, x::CoDual...)
 
 Equivalent to `value_and_pullback(rule, 1.0, f, x...)` -- assumes `f` returns a `Float64`.
 """
-function value_and_gradient!!(rule::R, fx::Vararg{CoDual, N}) where {R, N}
-    return value_and_pullback!!(rule, 1.0, fx...)
+function __value_and_gradient!!(rule::R, fx::Vararg{CoDual, N}) where {R, N}
+    return __value_and_pullback!!(rule, 1.0, fx...)
 end
 
 """
     value_and_pullback!!(rule, ȳ, f, x...)
 
-Compute the value and pullback of `f(x...)`.
+Compute the value and pullback of `f(x...)`. `ȳ` must be a valid tangent for the primal
+return by `f(x...)`.
 
 `rule` should be constructed using `build_rrule`.
 
@@ -45,10 +46,10 @@ will yield the wrong result.
 *Note:* This method of `value_and_pullback!!` has to first call `zero_codual` on all of its
 arguments. This may cause some additional allocations. If this is a problem in your
 use-case, consider pre-allocating the `CoDual`s and calling the other method of this
-function.
+function. The `CoDual`s should be primal-tangent pairs (as opposed to primal-fdata pairs).
 """
 function value_and_pullback!!(rule::R, ȳ, fx::Vararg{Any, N}) where {R, N}
-    return value_and_pullback!!(rule, ȳ, map(zero_fcodual, fx)...)
+    return __value_and_pullback!!(rule, ȳ, tuple_map(zero_codual, fx)...)
 end
 
 """
@@ -57,5 +58,5 @@ end
 Equivalent to `value_and_pullback(rule, 1.0, f, x...)` -- assumes `f` returns a `Float64`.
 """
 function value_and_gradient!!(rule::R, fx::Vararg{Any, N}) where {R, N}
-    return value_and_gradient!!(rule, map(zero_fcodual, fx)...)
+    return __value_and_gradient!!(rule, tuple_map(zero_codual, fx)...)
 end
diff --git a/test/interface.jl b/test/interface.jl
index 94c35d659..745194507 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -2,9 +2,14 @@
     @testset "$(typeof((f, x...)))" for (ȳ, f, x...) in Any[
         (1.0, (x, y) -> x * y + sin(x) * cos(y), 5.0, 4.0),
         ([1.0, 1.0], x -> [sin(x), sin(2x)], 3.0),
+        (1.0, x -> sum(5x), [5.0, 2.0]),
     ]
         rule = build_rrule(f, x...)
-        v, grad2 = value_and_pullback!!(rule, ȳ, f, x...)
+        v, (df, dx...) = value_and_pullback!!(rule, ȳ, f, x...)
         @test v ≈ f(x...)
+        @test df isa tangent_type(typeof(f))
+        for (_dx, _x) in zip(dx, x)
+            @test _dx isa tangent_type(typeof(_x))
+        end
     end
 end