diff --git a/Project.toml b/Project.toml
index 78f8cae..6f17776 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "AdvancedMH"
 uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
-version = "0.6.0"
+version = "0.6.1"
 
 [deps]
 AbstractMCMC = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
diff --git a/src/MALA.jl b/src/MALA.jl
index abb789d..f7a2a03 100644
--- a/src/MALA.jl
+++ b/src/MALA.jl
@@ -19,48 +19,60 @@ struct GradientTransition{T<:Union{Vector, Real, NamedTuple}, L<:Real, G<:Union{
     gradient::G
 end
 
-transition(::MALA, model, params) = GradientTransition(model, params)
-
-# Store the new draw, its log density and its gradient
-GradientTransition(model::DensityModel, params) = GradientTransition(params, logdensity_and_gradient(model, params)...)
+logdensity(model::DensityModel, t::GradientTransition) = t.lp
 
 propose(rng::Random.AbstractRNG, ::MALA, model) = error("please specify initial parameters")
+function transition(sampler::MALA, model::DensityModel, params)
+    return GradientTransition(params, logdensity_and_gradient(model, params)...)
+end
 
-function propose(
+function AbstractMCMC.step(
     rng::Random.AbstractRNG,
-    spl::MALA{<:Proposal},
     model::DensityModel,
-    params_prev::GradientTransition
-)
-    proposal = propose(rng, spl.proposal(params_prev.gradient), model, params_prev.params)
-    return GradientTransition(model, proposal)
-end
-
-
-function q(
-    spl::MALA{<:Proposal},
-    t::GradientTransition,
-    t_cond::GradientTransition
-)
-    return q(spl.proposal(-t_cond.gradient), t.params, t_cond.params)
-end
-
-function logratio_proposal_density(
-    sampler::MALA{<:Proposal}, state::GradientTransition, candidate::GradientTransition
+    sampler::MALA,
+    transition_prev::GradientTransition;
+    kwargs...
 )
-    return q(sampler, state, candidate) - q(sampler, candidate, state)
+    # Extract value and gradient of the log density of the current state.
+    state = transition_prev.params
+    logdensity_state = transition_prev.lp
+    gradient_logdensity_state = transition_prev.gradient
+
+    # Generate a new proposal.
+    proposal = sampler.proposal
+    candidate = propose(rng, proposal(gradient_logdensity_state), model, state)
+
+    # Compute both the value of the log density and its gradient
+    logdensity_candidate, gradient_logdensity_candidate = logdensity_and_gradient(
+        model, candidate
+    )
+
+    # Compute the log ratio of proposal densities.
+    logratio_proposal_density = q(
+        proposal(-gradient_logdensity_candidate), state, candidate
+    ) - q(proposal(-gradient_logdensity_state), candidate, state)
+
+    # Compute the log acceptance probability.
+    logα = logdensity_candidate - logdensity_state + logratio_proposal_density
+
+    # Decide whether to return the previous params or the new one.
+    transition = if -Random.randexp(rng) < logα
+        GradientTransition(candidate, logdensity_candidate, gradient_logdensity_candidate)
+    else
+        transition_prev
+    end
+
+    return transition, transition
 end
 
 """
     logdensity_and_gradient(model::DensityModel, params)
 
-Efficiently returns the value and gradient of the model
+Return the value and gradient of the log density of the parameters `params` for the `model`.
 """
 function logdensity_and_gradient(model::DensityModel, params)
     res = GradientResult(params)
     gradient!(res, model.logdensity, params)
-    return (value(res), gradient(res))
+    return value(res), gradient(res)
 end
 
-
-logdensity(model::DensityModel, t::GradientTransition) = t.lp
diff --git a/src/emcee.jl b/src/emcee.jl
index 28fb81d..2504122 100644
--- a/src/emcee.jl
+++ b/src/emcee.jl
@@ -3,23 +3,8 @@ struct Ensemble{D} <: MHSampler
     proposal::D
 end
 
-# Define the first sampling step.
-# Return a 2-tuple consisting of the initial sample and the initial state.
-# In this case they are identical.
-function AbstractMCMC.step(
-    rng::Random.AbstractRNG,
-    model::DensityModel,
-    spl::Ensemble;
-    init_params = nothing,
-    kwargs...,
-)
-    if init_params === nothing
-        transitions = propose(rng, spl, model)
-    else
-        transitions = [Transition(model, x) for x in init_params]
-    end
-
-    return transitions, transitions
+function transition(sampler::Ensemble, model::DensityModel, params)
+    return [Transition(model, x) for x in params]
 end
 
 # Define the other sampling steps.
diff --git a/src/mh-core.jl b/src/mh-core.jl
index cd195ce..def5553 100644
--- a/src/mh-core.jl
+++ b/src/mh-core.jl
@@ -48,115 +48,38 @@ end
 StaticMH(d) = MetropolisHastings(StaticProposal(d))
 RWMH(d) = MetropolisHastings(RandomWalkProposal(d))
 
-# default function without RNG
-propose(spl::MetropolisHastings, args...) = propose(Random.GLOBAL_RNG, spl, args...)
-
-# Propose from a vector of proposals
-function propose(
-    rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:AbstractArray},
-    model::DensityModel
-)
-    proposal = map(p -> propose(rng, p, model), spl.proposal)
-    return Transition(model, proposal)
-end
-
-function propose(
-    rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:AbstractArray},
-    model::DensityModel,
-    params_prev::Transition
-)
-    proposal = map(spl.proposal, params_prev.params) do p, params
-        propose(rng, p, model, params)
-    end
-    return Transition(model, proposal)
-end
-
-# Make a proposal from one Proposal struct.
-function propose(
-    rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:Proposal},
-    model::DensityModel
-)
-    proposal = propose(rng, spl.proposal, model)
-    return Transition(model, proposal)
-end
-
-function propose(
-    rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:Proposal},
-    model::DensityModel,
-    params_prev::Transition
-)
-    proposal = propose(rng, spl.proposal, model, params_prev.params)
-    return Transition(model, proposal)
-end
-
-# Make a proposal from a NamedTuple of Proposal.
-function propose(
-    rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:NamedTuple},
-    model::DensityModel
-)
-    proposal = _propose(rng, spl.proposal, model)
-    return Transition(model, proposal)
+function propose(rng::Random.AbstractRNG, sampler::MHSampler, model::DensityModel)
+    return propose(rng, sampler.proposal, model)
 end
-
 function propose(
     rng::Random.AbstractRNG,
-    spl::MetropolisHastings{<:NamedTuple},
+    sampler::MHSampler,
     model::DensityModel,
-    params_prev::Transition
+    transition_prev::Transition,
 )
-    proposal = _propose(rng, spl.proposal, model, params_prev.params)
-    return Transition(model, proposal)
+    return propose(rng, sampler.proposal, model, transition_prev.params)
 end
 
-@generated function _propose(
-    rng::Random.AbstractRNG,
-    proposal::NamedTuple{names},
-    model::DensityModel
-) where {names}
-    isempty(names) && return :(NamedTuple())
-    expr = Expr(:tuple)
-    expr.args = Any[:($name = propose(rng, proposal.$name, model)) for name in names]
-    return expr
+function transition(sampler::MHSampler, model::DensityModel, params)
+    logdensity = AdvancedMH.logdensity(model, params)
+    return transition(sampler, model, params, logdensity)
 end
-
-@generated function _propose(
-    rng::Random.AbstractRNG,
-    proposal::NamedTuple{names},
-    model::DensityModel,
-    params_prev::NamedTuple
-) where {names}
-    isempty(names) && return :(NamedTuple())
-    expr = Expr(:tuple)
-    expr.args = Any[
-        :($name = propose(rng, proposal.$name, model, params_prev.$name)) for name in names
-    ]
-    return expr
+function transition(sampler::MHSampler, model::DensityModel, params, logdensity::Real)
+    return Transition(params, logdensity)
 end
 
-transition(sampler, model, params) = transition(model, params)
-transition(model, params) = Transition(model, params)
-
 # Define the first sampling step.
 # Return a 2-tuple consisting of the initial sample and the initial state.
 # In this case they are identical.
 function AbstractMCMC.step(
     rng::Random.AbstractRNG,
     model::DensityModel,
-    spl::MHSampler;
+    sampler::MHSampler;
     init_params=nothing,
     kwargs...
 )
-    if init_params === nothing
-        transition = propose(rng, spl, model)
-    else
-        transition = AdvancedMH.transition(spl, model, init_params)
-    end
-
+    params = init_params === nothing ? propose(rng, sampler, model) : init_params
+    transition = AdvancedMH.transition(sampler, model, params)
     return transition, transition
 end
 
@@ -167,27 +90,30 @@ end
 function AbstractMCMC.step(
     rng::Random.AbstractRNG,
     model::DensityModel,
-    spl::MHSampler,
-    params_prev::AbstractTransition;
+    sampler::MHSampler,
+    transition_prev::AbstractTransition;
     kwargs...
 )
     # Generate a new proposal.
-    params = propose(rng, spl, model, params_prev)
+    candidate = propose(rng, sampler, model, transition_prev)
 
-    # Calculate the log acceptance probability.
-    logα = logdensity(model, params) - logdensity(model, params_prev) +
-        logratio_proposal_density(spl, params_prev, params)
+    # Calculate the log acceptance probability and the log density of the candidate.
+    logdensity_candidate = logdensity(model, candidate)
+    logα = logdensity_candidate - logdensity(model, transition_prev) +
+        logratio_proposal_density(sampler, transition_prev, candidate)
 
     # Decide whether to return the previous params or the new one.
-    if -Random.randexp(rng) < logα
-        return params, params
+    transition = if -Random.randexp(rng) < logα
+        AdvancedMH.transition(sampler, model, candidate, logdensity_candidate)
     else
-        return params_prev, params_prev
+        transition_prev
     end
+
+    return transition, transition
 end
 
 function logratio_proposal_density(
-    sampler::MetropolisHastings, params_prev::Transition, params::Transition
+    sampler::MetropolisHastings, transition_prev::AbstractTransition, candidate
 )
-    return logratio_proposal_density(sampler.proposal, params_prev.params, params.params)
+    return logratio_proposal_density(sampler.proposal, transition_prev.params, candidate)
 end
diff --git a/src/proposal.jl b/src/proposal.jl
index 13f3bf0..c02e5f7 100644
--- a/src/proposal.jl
+++ b/src/proposal.jl
@@ -125,6 +125,55 @@ function q(
     return q(proposal(t_cond), t, t_cond)
 end
 
+####################
+# Multiple proposals
+####################
+
+function propose(
+    rng::Random.AbstractRNG,
+    proposals::AbstractArray{<:Proposal},
+    model::DensityModel,
+)
+    return map(proposals) do proposal
+        return propose(rng, proposal, model)
+    end
+end
+function propose(
+    rng::Random.AbstractRNG,
+    proposals::AbstractArray{<:Proposal},
+    model::DensityModel,
+    ts,
+)
+    return map(proposals, ts) do proposal, t
+        return propose(rng, proposal, model, t)
+    end
+end
+
+@generated function propose(
+    rng::Random.AbstractRNG,
+    proposals::NamedTuple{names},
+    model::DensityModel,
+) where {names}
+    isempty(names) && return :(NamedTuple())
+    expr = Expr(:tuple)
+    expr.args = Any[:($name = propose(rng, proposals.$name, model)) for name in names]
+    return expr
+end
+
+@generated function propose(
+    rng::Random.AbstractRNG,
+    proposals::NamedTuple{names},
+    model::DensityModel,
+    ts,
+) where {names}
+    isempty(names) && return :(NamedTuple())
+    expr = Expr(:tuple)
+    expr.args = Any[
+        :($name = propose(rng, proposals.$name, model, ts.$name)) for name in names
+    ]
+    return expr
+end
+
 """
     logratio_proposal_density(proposal, state, candidate)