diff --git a/docs/src/api.md b/docs/src/api.md
index 1017af94..ad00a2aa 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -35,6 +35,8 @@ Optimisers.setup
 Optimisers.update
 Optimisers.update!
 Optimisers.adjust(::Any, ::Real)
+Optimisers.freeze!
+Optimisers.thaw!
 ```
 
 Calling `Functors.@functor` on your model's layer types by default causes
diff --git a/docs/src/index.md b/docs/src/index.md
index 65b441bb..659ae837 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -138,6 +138,33 @@ Optimisers.trainable(x::Layer) = (; alpha = x.alpha)  # must be a subset of chid
 st = Optimisers.setup(DecayDescent(0.1), Layer(3))
 ```
 
+## Frozen Parameters
+
+To temporarily prevent training from affecting some parameters,
+use [freeze!](@ref Optimisers.freeze!) and `thaw!`.
+They work by mutating all `Leaf`s of the state tree, or part of it.
+
+```julia
+using Flux, Optimisers
+
+x = randn(Float32, 28, 28, 1, 1);
+net = @autosize (size(x)...,) Chain(
+  Conv((3, 3), 1 => 3, stride=2, bias=false), Flux.flatten, Dense(_ => 2, relu),
+)
+opt = Optimisers.setup(Optimisers.Momentum(), net);
+
+net.layers[3] isa Dense  # now freeze this layer's parameters:
+Optimisers.freeze!(opt.layers[3])
+opt.layers[3].bias  # confirm: Leaf(Momentum(...), [0.0, 0.0], frozen = true)
+
+Optimisers.update!(opt, net, gradient(m -> sum(m(x)), net)...);
+
+net.layers[3].bias  # stil zero, and its momentum is too:
+
+Optimisers.thaw!(opt)
+opt.layers[3].bias  # Leaf(Momentum(...), [0.0, 0.0])
+```
+
 ## Tied Parameters
 
 If the same array appears twice (or more) in the model, [Functors.jl](https://fluxml.ai/Functors.jl) should recognise this.
@@ -159,7 +186,7 @@ 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
 
diff --git a/src/adjust.jl b/src/adjust.jl
index 78b3d452..a8123676 100644
--- a/src/adjust.jl
+++ b/src/adjust.jl
@@ -1,3 +1,59 @@
+###
+### freezing
+###
+
+"""
+    Optimisers.freeze!(tree)
+
+Temporarily alters the state `tree = setup(rule, model)` so that parameters
+will not be updated. Un-done by [`thaw!`](@ref Optimisers.thaw!).
+
+Can be applied to the state corresponding to only part of a model,
+for instance with `model::Chain`, to freeze `model.layers[1]` you
+should call `freeze!(tree.layers[1])`.
+
+# Example
+```jldoctest
+julia> m = (x = ([1.0], 2.0), y = [3.0]);
+
+julia> s = Optimisers.setup(Momentum(), m);
+
+julia> Optimisers.freeze!(s.x)
+
+julia> Optimisers.update!(s, m, (x = ([pi], 10pi), y = [100pi]));  # with fake gradient
+
+julia> m
+(x = ([1.0], 2.0), y = [-0.14159258336972558])
+
+julia> s
+(x = (Leaf(Momentum{Float32}(0.01, 0.9), [0.0], frozen = true), ()), y = Leaf(Momentum{Float32}(0.01, 0.9), [3.14159]))
+
+julia> Optimisers.thaw!(s)
+
+julia> s.x
+(Leaf(Momentum{Float32}(0.01, 0.9), [0.0]), ())
+```
+"""
+freeze!(tree) = foreach(freeze!, tree)
+freeze!(ℓ::Leaf) = (ℓ.frozen = true; nothing)
+
+"""
+    Optimisers.thaw!(tree)
+
+The reverse of [`freeze!`](@ref Optimisers.freeze!). Applies to all parameters,
+mutating every `Leaf(rule, state, frozen = true)` to `Leaf(rule, state, frozen = false)`.
+"""
+thaw!(tree) = foreach(thaw!, tree)
+thaw!(ℓ::Leaf) = (ℓ.frozen = false; nothing)
+
+freeze!(::Union{Number, AbstractArray{<:Number}}) = throw(ArgumentError(
+  "`freeze!` must not be applied to a model, only to the state tree from `setup`"))
+thaw!(::Union{Number, AbstractArray{<:Number}}) = throw(ArgumentError(
+  "`thaw!` must not be applied to a model, only to the state tree from `setup`"))
+
+###
+### adjust
+###
 
 """
     Optimisers.adjust(tree, η) -> tree
@@ -47,8 +103,8 @@ adjust(tree; kw...) = map(st -> adjust(st; kw...), tree)
 adjust(::Nothing, ::Real) = nothing
 adjust(::Nothing; kw...) = nothing
 
-adjust(ℓ::Leaf, eta::Real) = Leaf(adjust(ℓ.rule, eta), ℓ.state)
-adjust(ℓ::Leaf; kw...) = Leaf(adjust(ℓ.rule; kw...), ℓ.state)
+adjust(ℓ::Leaf, eta::Real) = Leaf(adjust(ℓ.rule, eta), ℓ.state, ℓ.frozen)
+adjust(ℓ::Leaf; kw...) = Leaf(adjust(ℓ.rule; kw...), ℓ.state, ℓ.frozen)
 
 
 """
diff --git a/src/interface.jl b/src/interface.jl
index 79d03396..401c9b1c 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -10,10 +10,12 @@ abstract type AbstractRule end
 ### setup
 ###
 
-mutable struct Leaf{R,S}  # mutable so that its identity encodes parameter sharing
+mutable struct Leaf{R,S}  # mutable so that its identity encodes parameter sharing...
   rule::R
   state::S
+  frozen::Bool  # ... and to allow freeze! to act on this.
 end
+Leaf(rule, state; frozen::Bool = false) = Leaf(rule, state, frozen)
 
 @functor Leaf
 
@@ -42,11 +44,12 @@ function _setup(rule, x; cache)
   end
 end
 
-function Base.show(io::IO, ℓ::Leaf)  # show method is mostly to hide its long type!
+function Base.show(io::IO, ℓ::Leaf; colour = ℓ.frozen ? :cyan : :green)
   ioc = IOContext(io, :compact => true)
-  print(ioc, "Leaf(", ℓ.rule, ", ")
+  str = sprint(show, ℓ.rule; context = ioc)  # produces Adam{Float32}(0.001, ... not 0.001f0
+  printstyled(io, "Leaf(", str, ", "; color = colour)
   show(ioc, ℓ.state)
-  print(ioc, ")")
+  printstyled(io, ℓ.frozen ? ", frozen = true)" : ")"; color = colour)
 end
 
 ###
@@ -83,6 +86,7 @@ function _update!(tree, x; grads, params)
 end
 function _update!(ℓ::Leaf, x; grads, params)
   haskey(params, (ℓ,x)) && return params[(ℓ,x)]
+  ℓ.frozen && return x
   params[(ℓ,x)] = if haskey(grads, ℓ)
     ℓ.state, x̄′ = apply!(ℓ.rule, ℓ.state, x, grads[ℓ]...)
     subtract!(x, x̄′)
diff --git a/test/runtests.jl b/test/runtests.jl
index 51e76053..a8cef6f6 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -221,6 +221,24 @@ end
       @test sc2.γ.state[2][1] ≈ [0.1, 0.2, 0.2]
     end
 
+    @testset "freeze/thaw" begin
+      m = (x=[1.0, 2.0], y=([3.0, 4.0], sin));
+      st = Optimisers.setup(Descent(0.1), m);
+      Optimisers.freeze!(st.y)
+      st, m = Optimisers.update(st, m, (x=[1,10], y=([100,1000], nothing)));
+      @test m.x ≈ [0.9, 1.0]
+      @test m.y[1] == [3, 4]
+
+      st = Optimisers.adjust(st, 0.2)
+      Optimisers.thaw!(st)
+      st, m = Optimisers.update(st, m, (x=[1,10], y=([100,1000], nothing)));
+      @test m.y[1] ≈ [-17.0, -196.0]
+      @test m.x ≈ [0.7, -1.0]
+
+      @test_throws ArgumentError Optimisers.freeze!(m)
+      @test_throws ArgumentError Optimisers.thaw!(m)
+    end
+
     @testset "forgotten gradient" begin
       x = [1.0, 2.0]
       sx = Optimisers.setup(Descent(), x)