diff --git a/Project.toml b/Project.toml
index f1d8501e..bac796ea 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Optimisers"
 uuid = "3bd65402-5787-11e9-1adc-39752487f4e2"
 authors = ["Mike J Innes <mike.j.innes@gmail.com>"]
-version = "0.2.9"
+version = "0.2.10"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -12,7 +12,7 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 ChainRulesCore = "1"
-Functors = "0.2.8, 0.3"
+Functors = "0.3"
 Zygote = "0.6.40"
 julia = "1.6"
 
diff --git a/docs/src/index.md b/docs/src/index.md
index aaee5d7f..65b441bb 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,6 +1,6 @@
 # Optimisers.jl
 
-## Defining an optimisation rule
+## An optimisation rule
 
 A new optimiser must overload two functions, [`apply!`](@ref) and [`init`](@ref).
 These act on one array of parameters:
@@ -60,6 +60,11 @@ Notice that a completely new instance of the model is returned. Internally, this
 is handled by [Functors.jl](https://fluxml.ai/Functors.jl), where we do a walk over the
 tree formed by the model and update the parameters using the gradients.
 
+There is also [`Optimisers.update!`](@ref) which similarly returns a new model and new state,
+but is free to mutate arrays within the old one for efficiency.
+The method of `apply!` for each rule is likewise free to mutate arrays within its state;
+they are defensively copied when this rule is used with `update`.
+
 Optimisers.jl does not depend on any one automatic differentiation package,
 but for now the most likely source of gradients is [Zygote.jl](https://fluxml.ai/Zygote.jl).
 Note that `update` always wants the gradient from Zygote's "explicit" mode, as shown above.
@@ -67,11 +72,6 @@ This `∇model` is another tree structure, rather than the dictionary-like objec
 Zygote's "implicit" mode `gradient(() -> loss(...), Flux.params(model))` -- see 
 [Zygote's documentation](https://fluxml.ai/Zygote.jl/dev/#Explicit-and-Implicit-Parameters-1) for more about this difference.
 
-There is also [`Optimisers.update!`](@ref) which similarly returns a new model and new state,
-but is free to mutate arrays within the old one for efficiency.
-The method of `apply!` you write is likewise free to mutate arrays within its state;
-they are defensively copied when this rule is used with `update`.
-
 ## Usage with [Lux.jl](https://github.com/avik-pal/Lux.jl)
 
 The main design difference of Lux is that the tree of parameters is separate from
@@ -110,6 +110,57 @@ Besides the parameters stored in `params` and gradually optimised, any other mod
 is stored in `lux_state`. For simplicity this example does not show how to propagate the 
 updated `lux_state` to the next iteration, see Lux's documentation.
 
+## Non-`trainable` Parameters
+
+Optimisers.jl uses [Functors.jl](https://fluxml.ai/Functors.jl) to walk the `struct`s
+making up the model, for which they must be annotated `@functor Type`. 
+By default optimisation will alter all [`isnumeric`](@ref) arrays. 
+
+If some arrays of a particular layer should not be treated this way,
+you can define a method for [`trainable`](@ref)
+
+```julia
+struct Layer{T}
+  alpha::T
+  beta::T
+  length::Int
+end
+Layer(n::Int) = Layer(randn(n), zeros(n), n)
+
+Functors.@functor Layer
+
+# Both array fields will be, for example, moved to the GPU:
+Functors.children(Layer(3))  # (alpha = [...], beta = [...], length)
+
+Optimisers.trainable(x::Layer) = (; alpha = x.alpha)  # must be a subset of chidlren
+
+# Only the first field will be optimised:
+st = Optimisers.setup(DecayDescent(0.1), Layer(3))
+```
+
+## Tied Parameters
+
+If the same array appears twice (or more) in the model, [Functors.jl](https://fluxml.ai/Functors.jl) should recognise this.
+Within Optimisers.jl, `setup` will initialise once, and use the same `Leaf` for both parameters. 
+Then `update` will accumulate the gradient from both, and the updated model returned will have the tie maintained.
+
+```julia
+using Flux, Optimisers
+
+enc = Chain(Dense(40 => 20, tanh), Dense(20 => 10));
+dec = Chain(Dense(enc[1].weight', true, tanh), Dense(enc[2].weight', true, tanh));
+model = Chain(; enc, dec)
+
+st = Optimisers.setup(Optimisers.Adam(), model);
+
+st.layers.enc.layers[1].weight === st.layers.dec.layers[1].weight.parent  # true
+```
+
+This identification relies on `===`, and will work for ordinary `Array`s and `CuArray`s.
+It will not at present work for `reshape`d arrays, nor for immutable arrays such as those
+from StaticArrays.jl.
+ 
+ 
 ## Obtaining a flat parameter vector
 
 Instead of a nested tree-like structure, sometimes is is convenient to have all the
@@ -143,10 +194,11 @@ st, flat = Optimisers.update(st, flat, ∇flat)
 ```
 
 Here `flat` contains only the 283 trainable parameters, while the non-trainable
-ones are preserved inside `re`.
+ones are preserved inside `re`, an object of type `Restructure`.
 When defining new layers, these can be specified if necessary by overloading [`trainable`](@ref).
 By default, all numeric arrays visible to [Functors.jl](https://github.com/FluxML/Functors.jl)
 are assumed to contain trainable parameters.
+Tied parameters (arrays appearing in different layers) are included only once in `flat`.
 
 Lux stores only the trainable parameters in `params`.
 This can also be flattened to a plain `Vector` in the same way:
diff --git a/src/Optimisers.jl b/src/Optimisers.jl
index 7c94e233..73c56305 100644
--- a/src/Optimisers.jl
+++ b/src/Optimisers.jl
@@ -16,6 +16,10 @@ export Descent, Adam, Momentum, Nesterov, Rprop, RMSProp,
        AdaGrad, AdaMax, AdaDelta, AMSGrad, NAdam, AdamW, RAdam, OAdam, AdaBelief,
        WeightDecay, ClipGrad, ClipNorm, OptimiserChain
 
+###
+### one-array functions
+###
+
 """
     Optimisers.apply!(rule::RuleType, state, parameters, gradient) -> (state, gradient)
 
@@ -57,6 +61,10 @@ julia> Optimisers.init(Momentum(), [1.0, 2.0])
 """
 init
 
+###
+### whole-model functions
+###
+
 """
     Optimisers.setup(rule, model) -> tree
 
diff --git a/src/interface.jl b/src/interface.jl
index 1903d615..79d03396 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -166,7 +166,7 @@ end
 ###
 
 """
-    @.. x = x + y
+    @.. x = y + z
 
 Sometimes in-place broadcasting macro, for use in `apply!` rules.
 If `maywrite(x)` then it is just `@. x = rhs`, but if not, it becomes `x = @. rhs`.