diff --git a/Project.toml b/Project.toml
index 02e13b7..7422f28 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 = "0.3.1"
+version = "0.3.2"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/Optimisers.jl b/src/Optimisers.jl
index 1451bc8..9254bb7 100644
--- a/src/Optimisers.jl
+++ b/src/Optimisers.jl
@@ -14,7 +14,7 @@ export destructure
 include("rules.jl")
 export Descent, Adam, Momentum, Nesterov, Rprop, RMSProp,
        AdaGrad, AdaMax, AdaDelta, AMSGrad, NAdam, AdamW, RAdam, OAdam, AdaBelief,
-       WeightDecay, ClipGrad, ClipNorm, OptimiserChain, Lion,
+       WeightDecay, SignDecay, ClipGrad, ClipNorm, OptimiserChain, Lion,
        AccumGrad
 
 ###
diff --git a/src/rules.jl b/src/rules.jl
index ecc5860..9fa5011 100644
--- a/src/rules.jl
+++ b/src/rules.jl
@@ -487,7 +487,7 @@ function apply!(o::NAdam, state, x::AbstractArray{T}, dx) where T
 end
 
 """
-    AdamW(η = 0.001, β = (0.9, 0.999), γ = 0, ϵ = 1e-8)
+    AdamW(η = 0.001, β = (0.9, 0.999), λ = 0, ϵ = 1e-8)
 
 [AdamW](https://arxiv.org/abs/1711.05101) is a variant of Adam fixing (as in repairing) its
 weight decay regularization.
@@ -497,12 +497,12 @@ weight decay regularization.
                        the weights.
 - Decay of momentums (`β::Tuple`): Exponential decay for the first (β1) and the
                                    second (β2) momentum estimate.
-- Weight decay (`γ`): Decay applied to weights during optimisation.
+- Weight decay (`λ`): Controls the strength of ``L_2`` regularisation.
 - Machine epsilon (`ϵ`): Constant to prevent division by zero
                          (no need to change default)
 """
-AdamW(η = 0.001, β = (0.9, 0.999), γ = 0, ϵ = 1e-8) =
-  OptimiserChain(Adam(η, β, ϵ), WeightDecay(γ))
+AdamW(η = 0.001, β = (0.9, 0.999), λ = 0, ϵ = 1e-8) =
+  OptimiserChain(Adam(η, β, ϵ), WeightDecay(λ))
 
 """
     AdaBelief(η = 0.001, β = (0.9, 0.999), ϵ = 1e-16)
@@ -538,35 +538,79 @@ function apply!(o::AdaBelief, state, x::AbstractArray{T}, dx) where T
 end
 
 """
-    WeightDecay(γ = 5e-4)
+    WeightDecay(λ = 5e-4)
 
-Decay weights by ``γ``, that is, add `γ .* x` to the gradient `x̄` which will be
-subtracted from `x`.
+Implements ``L_2`` regularisation, also known as ridge regression, 
+when composed  with other rules as the first transformation in an [`OptimiserChain`](@ref).
 
-Typically composed  with other optimisers as the first transformation in an [`OptimiserChain`](@ref).
-This is equivalent to adding ``L_2`` regularization with coefficient ``γ`` to the loss.
+It does this by adding `λ .* x` to the gradient. This is equivalent to adding 
+`λ/2 * sum(abs2, x) == λ/2 * norm(x)^2` to the loss.
+
+See also [`SignDecay`] for ``L_1`` normalisation.
 
 # Parameters
-- Weight decay (`γ`): Decay applied to weights during optimisation.
+- Penalty (`λ ≥ 0`): Controls the strength of the regularisation.
 """
 @def struct WeightDecay <: AbstractRule
-  gamma = 5e-4
+  lambda = 5e-4
 end
 
 init(o::WeightDecay, x::AbstractArray) = nothing
 
 function apply!(o::WeightDecay, state, x::AbstractArray{T}, dx) where T
-  γ = T(o.gamma)
-  dx′ = @lazy dx + γ * x
+  λ = T(o.lambda)
+  dx′ = @lazy dx + λ * x
 
   return state, dx′
 end
 
+function adjust(r::WeightDecay; gamma = nothing, kw...)
+   if isnothing(gamma)
+     return _adjust(r, NamedTuple(kw))
+   else
+     Base.depwarn("The strength of WeightDecay is now field :lambda, not :gamma", :adjust, force=true)
+     nt = (; lambda = gamma, NamedTuple(kw)...)
+     return _adjust(r, nt)
+   end
+ end
+
+"""
+    SignDecay(λ = 1e-3)
+
+Implements ``L_1`` regularisation, also known as LASSO regression,
+when composed  with other rules as the first transformation in an [`OptimiserChain`](@ref).
+
+It does this by adding `λ .* sign(x)` to the gradient. This is equivalent to adding 
+`λ * sum(abs, x) == λ * norm(x, 1)` to the loss.
+
+See also [`WeightDecay`] for ``L_2`` normalisation.
+They can be used together: `OptimiserChain(SignDecay(0.012), WeightDecay(0.034), Adam())`
+is equivalent to adding `0.012 * norm(x, 1) + 0.017 * norm(x, 2)^2` to the loss function.
+
+# Parameters
+- Penalty (`λ ≥ 0`): Controls the strength of the regularisation.
+"""
+@def struct SignDecay <: AbstractRule
+  lambda = 1e-3
+end
+
+init(o::SignDecay, x::AbstractArray) = nothing
+
+function apply!(o::SignDecay, state, x::AbstractArray{T}, dx) where T
+  λ = T(o.lambda)
+  dx′ = @lazy dx + λ * sign(x)
+
+  return state, dx′
+end
+
+
 """
     ClipGrad(δ = 10)
 
 Restricts every gradient component to obey `-δ ≤ dx[i] ≤ δ`.
 
+Typically composed with other rules using [`OptimiserChain`](@ref).
+
 See also [`ClipNorm`](@ref).
 """
 @def struct ClipGrad <: AbstractRule
@@ -591,6 +635,8 @@ to stay at this threshold (unless `p==0`).
 Throws an error if the norm is infinite or `NaN`,
 which you can turn off with `throw = false`.
 
+Typically composed with other rules using [`OptimiserChain`](@ref).
+
 See also [`ClipGrad`](@ref).
 """
 struct ClipNorm <: AbstractRule
diff --git a/test/rules.jl b/test/rules.jl
index 0ac2648..52a3580 100644
--- a/test/rules.jl
+++ b/test/rules.jl
@@ -10,7 +10,7 @@ RULES = [
   AdaGrad(), AdaMax(), AdaDelta(), AMSGrad(), NAdam(),
   AdamW(), RAdam(), OAdam(), AdaBelief(), Lion(),
   # A few chained combinations:
-  OptimiserChain(WeightDecay(), Adam(0.001)),
+  OptimiserChain(SignDecay(0.001), Adam(0.001)),
   OptimiserChain(ClipNorm(), Adam(0.001)),
   OptimiserChain(ClipGrad(0.5), Momentum()),
   OptimiserChain(WeightDecay(), OAdam(), ClipGrad(1)),
diff --git a/test/runtests.jl b/test/runtests.jl
index 49b595a..82d43bd 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -137,6 +137,7 @@ end
     @testset "OptimiserChain" begin
       x = [1, 10, 100.0]; dx = [1, 2, 3.0];
       @test Optimisers.update(Optimisers.setup(WeightDecay(0.1), x), x, dx)[2] ≈ [1-0.1-1, 10-1-2, 100-10-3]
+      @test Optimisers.update(Optimisers.setup(SignDecay(0.1), x), x, dx)[2] ≈ [1-0.1-1, 10-0.1-2, 100-0.1-3]
       @test Optimisers.update(Optimisers.setup(ClipGrad(2), x), x, dx)[2] ≈ [1-1, 10-2, 100-2]
 
       o2 = OptimiserChain(ClipGrad(2), WeightDecay(0.1))
@@ -154,6 +155,10 @@ end
 
       o0 = OptimiserChain()
       @test Optimisers.update(Optimisers.setup(o0, x), x, dx)[2] ≈ [1-1,10-2,100-3]
+
+      # L1 norm via sign
+      xm = [1, -10, 100.0]; dxm = [3, 2, -1];
+      @test Optimisers.update(Optimisers.setup(SignDecay(0.1), xm), xm, dxm)[2] ≈ [1-0.1-3, -10+0.1-2, 100-0.1+1]
     end
 
     @testset "trainable subset" begin