diff --git a/HISTORY.md b/HISTORY.md
index 91306c219..ff28349d8 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -32,9 +32,14 @@ You should not need to use these directly, please use `AbstractPPL.condition` an
 
 Removed the method `returned(::Model, values, keys)`; please use `returned(::Model, ::AbstractDict{<:VarName})` instead.
 
+The unexported functions `supports_varname_indexing(chain)`, `getindex_varname(chain)`, and `varnames(chain)` have been removed.
+
 The method `DynamicPPL.init` (for implementing `AbstractInitStrategy`) now has a different signature: it must return a tuple of the generated value, plus a transform function that maps it back to unlinked space.
 This is a generalisation of the previous behaviour, where `init` would always return an unlinked value (in effect forcing the transform to be the identity function).
 
+The family of functions `returned(model, chain)`, along with the same signatures of `pointwise_logdensities`, `logjoint`, `loglikelihood`, and `logprior`, have been changed such that if the chain does not contain all variables in the model, an error is thrown.
+Previously the behaviour would have been to sample missing variables.
+
 ## 0.38.9
 
 Remove warning when using Enzyme as the AD backend.
diff --git a/ext/DynamicPPLMCMCChainsExt.jl b/ext/DynamicPPLMCMCChainsExt.jl
index e74f0b8a9..8ad828648 100644
--- a/ext/DynamicPPLMCMCChainsExt.jl
+++ b/ext/DynamicPPLMCMCChainsExt.jl
@@ -1,41 +1,19 @@
 module DynamicPPLMCMCChainsExt
 
-using DynamicPPL: DynamicPPL, AbstractPPL, AbstractMCMC
+using DynamicPPL: DynamicPPL, AbstractPPL, AbstractMCMC, Random
 using MCMCChains: MCMCChains
 
-_has_varname_to_symbol(info::NamedTuple{names}) where {names} = :varname_to_symbol in names
-
-function DynamicPPL.supports_varname_indexing(chain::MCMCChains.Chains)
-    return _has_varname_to_symbol(chain.info)
-end
-
-function _check_varname_indexing(c::MCMCChains.Chains)
-    return DynamicPPL.supports_varname_indexing(c) ||
-           error("This `Chains` object does not support indexing using `VarName`s.")
-end
-
-function DynamicPPL.getindex_varname(
+function getindex_varname(
     c::MCMCChains.Chains, sample_idx, vn::DynamicPPL.VarName, chain_idx
 )
-    _check_varname_indexing(c)
     return c[sample_idx, c.info.varname_to_symbol[vn], chain_idx]
 end
-function DynamicPPL.varnames(c::MCMCChains.Chains)
-    _check_varname_indexing(c)
+function get_varnames(c::MCMCChains.Chains)
+    haskey(c.info, :varname_to_symbol) ||
+        error("This `Chains` object does not support indexing using `VarName`s.")
     return keys(c.info.varname_to_symbol)
 end
 
-function chain_sample_to_varname_dict(
-    c::MCMCChains.Chains{Tval}, sample_idx, chain_idx
-) where {Tval}
-    _check_varname_indexing(c)
-    d = Dict{DynamicPPL.VarName,Tval}()
-    for vn in DynamicPPL.varnames(c)
-        d[vn] = DynamicPPL.getindex_varname(c, sample_idx, vn, chain_idx)
-    end
-    return d
-end
-
 """
     AbstractMCMC.from_samples(
         ::Type{MCMCChains.Chains},
@@ -118,8 +96,8 @@ function AbstractMCMC.to_samples(
     # Get parameters
     params_matrix = map(idxs) do (sample_idx, chain_idx)
         d = DynamicPPL.OrderedCollections.OrderedDict{DynamicPPL.VarName,Any}()
-        for vn in DynamicPPL.varnames(chain)
-            d[vn] = DynamicPPL.getindex_varname(chain, sample_idx, vn, chain_idx)
+        for vn in get_varnames(chain)
+            d[vn] = getindex_varname(chain, sample_idx, vn, chain_idx)
         end
         d
     end
@@ -177,6 +155,46 @@ function AbstractMCMC.bundle_samples(
     return sort_chain ? sort(chain) : chain
 end
 
+"""
+    reevaluate_with_chain(
+        rng::AbstractRNG,
+        model::Model,
+        chain::MCMCChains.Chains
+        accs::NTuple{N,AbstractAccumulator};
+        fallback=nothing,
+    )
+
+Re-evaluate `model` for each sample in `chain` using the accumulators provided in `at`,
+returning an matrix of `(retval, updated_at)` tuples.
+
+This loops over all entries in the chain and uses `DynamicPPL.InitFromParams` as the
+initialisation strategy when re-evaluating the model. For many usecases the fallback should
+not be provided (as we expect the chain to contain all necessary variables); but for
+`predict` this has to be `InitFromPrior()` to allow sampling new variables (i.e. generating
+the posterior predictions).
+"""
+function reevaluate_with_chain(
+    rng::Random.AbstractRNG,
+    model::DynamicPPL.Model,
+    chain::MCMCChains.Chains,
+    accs::NTuple{N,DynamicPPL.AbstractAccumulator},
+    fallback::Union{DynamicPPL.AbstractInitStrategy,Nothing}=nothing,
+) where {N}
+    params_with_stats = AbstractMCMC.to_samples(DynamicPPL.ParamsWithStats, chain)
+    vi = DynamicPPL.OnlyAccsVarInfo(DynamicPPL.AccumulatorTuple(accs))
+    return map(params_with_stats) do ps
+        DynamicPPL.init!!(rng, model, vi, DynamicPPL.InitFromParams(ps.params, fallback))
+    end
+end
+function reevaluate_with_chain(
+    model::DynamicPPL.Model,
+    chain::MCMCChains.Chains,
+    accs::NTuple{N,DynamicPPL.AbstractAccumulator},
+    fallback::Union{DynamicPPL.AbstractInitStrategy,Nothing}=nothing,
+) where {N}
+    return reevaluate_with_chain(Random.default_rng(), model, chain, accs, fallback)
+end
+
 """
     predict([rng::AbstractRNG,] model::Model, chain::MCMCChains.Chains; include_all=false)
 
@@ -245,30 +263,18 @@ function DynamicPPL.predict(
     include_all=false,
 )
     parameter_only_chain = MCMCChains.get_sections(chain, :parameters)
-
-    # Set up a VarInfo with the right accumulators
-    varinfo = DynamicPPL.setaccs!!(
-        DynamicPPL.VarInfo(),
-        (
-            DynamicPPL.LogPriorAccumulator(),
-            DynamicPPL.LogLikelihoodAccumulator(),
-            DynamicPPL.ValuesAsInModelAccumulator(false),
-        ),
+    accs = (
+        DynamicPPL.LogPriorAccumulator(),
+        DynamicPPL.LogLikelihoodAccumulator(),
+        DynamicPPL.ValuesAsInModelAccumulator(false),
     )
-    _, varinfo = DynamicPPL.init!!(model, varinfo)
-    varinfo = DynamicPPL.typed_varinfo(varinfo)
-
-    params_and_stats = AbstractMCMC.to_samples(
-        DynamicPPL.ParamsWithStats, parameter_only_chain
+    predictions = map(
+        DynamicPPL.ParamsWithStats ∘ last,
+        reevaluate_with_chain(
+            rng, model, parameter_only_chain, accs, DynamicPPL.InitFromPrior()
+        ),
     )
-    predictions = map(params_and_stats) do ps
-        _, varinfo = DynamicPPL.init!!(
-            rng, model, varinfo, DynamicPPL.InitFromParams(ps.params)
-        )
-        DynamicPPL.ParamsWithStats(varinfo)
-    end
     chain_result = AbstractMCMC.from_samples(MCMCChains.Chains, predictions)
-
     parameter_names = if include_all
         MCMCChains.names(chain_result, :parameters)
     else
@@ -348,18 +354,7 @@ julia> returned(model, chain)
 """
 function DynamicPPL.returned(model::DynamicPPL.Model, chain_full::MCMCChains.Chains)
     chain = MCMCChains.get_sections(chain_full, :parameters)
-    varinfo = DynamicPPL.VarInfo(model)
-    iters = Iterators.product(1:size(chain, 1), 1:size(chain, 3))
-    params_with_stats = AbstractMCMC.to_samples(DynamicPPL.ParamsWithStats, chain)
-    return map(params_with_stats) do ps
-        first(
-            DynamicPPL.init!!(
-                model,
-                varinfo,
-                DynamicPPL.InitFromParams(ps.params, DynamicPPL.InitFromPrior()),
-            ),
-        )
-    end
+    return map(first, reevaluate_with_chain(model, chain, (), nothing))
 end
 
 """
@@ -452,24 +447,13 @@ function DynamicPPL.pointwise_logdensities(
     ::Type{Tout}=MCMCChains.Chains,
     ::Val{whichlogprob}=Val(:both),
 ) where {whichlogprob,Tout}
-    vi = DynamicPPL.VarInfo(model)
     acc = DynamicPPL.PointwiseLogProbAccumulator{whichlogprob}()
     accname = DynamicPPL.accumulator_name(acc)
-    vi = DynamicPPL.setaccs!!(vi, (acc,))
     parameter_only_chain = MCMCChains.get_sections(chain, :parameters)
-    iters = Iterators.product(1:size(chain, 1), 1:size(chain, 3))
-    pointwise_logps = map(iters) do (sample_idx, chain_idx)
-        # Extract values from the chain
-        values_dict = chain_sample_to_varname_dict(parameter_only_chain, sample_idx, chain_idx)
-        # Re-evaluate the model
-        _, vi = DynamicPPL.init!!(
-            model,
-            vi,
-            DynamicPPL.InitFromParams(values_dict, DynamicPPL.InitFromPrior()),
-        )
-        DynamicPPL.getacc(vi, Val(accname)).logps
-    end
-
+    pointwise_logps =
+        map(reevaluate_with_chain(model, parameter_only_chain, (acc,), nothing)) do (_, vi)
+            DynamicPPL.getacc(vi, Val(accname)).logps
+        end
     # pointwise_logps is a matrix of OrderedDicts
     all_keys = DynamicPPL.OrderedCollections.OrderedSet{DynamicPPL.VarName}()
     for d in pointwise_logps
@@ -556,15 +540,15 @@ julia> logjoint(demo_model([1., 2.]), chain)
 ```
 """
 function DynamicPPL.logjoint(model::DynamicPPL.Model, chain::MCMCChains.Chains)
-    var_info = DynamicPPL.VarInfo(model) # extract variables info from the model
-    map(Iterators.product(1:size(chain, 1), 1:size(chain, 3))) do (iteration_idx, chain_idx)
-        argvals_dict = DynamicPPL.OrderedCollections.OrderedDict{DynamicPPL.VarName,Any}(
-            vn_parent => DynamicPPL.values_from_chain(
-                var_info, vn_parent, chain, chain_idx, iteration_idx
-            ) for vn_parent in keys(var_info)
-        )
-        DynamicPPL.logjoint(model, argvals_dict)
-    end
+    return map(
+        DynamicPPL.getlogjoint ∘ last,
+        reevaluate_with_chain(
+            model,
+            chain,
+            (DynamicPPL.LogPriorAccumulator(), DynamicPPL.LogLikelihoodAccumulator()),
+            nothing,
+        ),
+    )
 end
 
 """
@@ -596,15 +580,12 @@ julia> loglikelihood(demo_model([1., 2.]), chain)
 ```
 """
 function DynamicPPL.loglikelihood(model::DynamicPPL.Model, chain::MCMCChains.Chains)
-    var_info = DynamicPPL.VarInfo(model) # extract variables info from the model
-    map(Iterators.product(1:size(chain, 1), 1:size(chain, 3))) do (iteration_idx, chain_idx)
-        argvals_dict = DynamicPPL.OrderedCollections.OrderedDict{DynamicPPL.VarName,Any}(
-            vn_parent => DynamicPPL.values_from_chain(
-                var_info, vn_parent, chain, chain_idx, iteration_idx
-            ) for vn_parent in keys(var_info)
-        )
-        DynamicPPL.loglikelihood(model, argvals_dict)
-    end
+    return map(
+        DynamicPPL.getloglikelihood ∘ last,
+        reevaluate_with_chain(
+            model, chain, (DynamicPPL.LogLikelihoodAccumulator(),), nothing
+        ),
+    )
 end
 
 """
@@ -637,15 +618,10 @@ julia> logprior(demo_model([1., 2.]), chain)
 ```
 """
 function DynamicPPL.logprior(model::DynamicPPL.Model, chain::MCMCChains.Chains)
-    var_info = DynamicPPL.VarInfo(model) # extract variables info from the model
-    map(Iterators.product(1:size(chain, 1), 1:size(chain, 3))) do (iteration_idx, chain_idx)
-        argvals_dict = DynamicPPL.OrderedCollections.OrderedDict{DynamicPPL.VarName,Any}(
-            vn_parent => DynamicPPL.values_from_chain(
-                var_info, vn_parent, chain, chain_idx, iteration_idx
-            ) for vn_parent in keys(var_info)
-        )
-        DynamicPPL.logprior(model, argvals_dict)
-    end
+    return map(
+        DynamicPPL.getlogprior ∘ last,
+        reevaluate_with_chain(model, chain, (DynamicPPL.LogPriorAccumulator(),), nothing),
+    )
 end
 
 end
diff --git a/src/chains.jl b/src/chains.jl
index f176b8e68..2fcd4e713 100644
--- a/src/chains.jl
+++ b/src/chains.jl
@@ -1,29 +1,3 @@
-"""
-    supports_varname_indexing(chain::AbstractChains)
-
-Return `true` if `chain` supports indexing using `VarName` in place of the
-variable name index.
-"""
-supports_varname_indexing(::AbstractChains) = false
-
-"""
-    getindex_varname(chain::AbstractChains, sample_idx, varname::VarName, chain_idx)
-
-Return the value of `varname` in `chain` at `sample_idx` and `chain_idx`.
-
-Whether this method is implemented for `chains` is indicated by [`supports_varname_indexing`](@ref).
-"""
-function getindex_varname end
-
-"""
-    varnames(chains::AbstractChains)
-
-Return an iterator over the varnames present in `chains`.
-
-Whether this method is implemented for `chains` is indicated by [`supports_varname_indexing`](@ref).
-"""
-function varnames end
-
 """
     ParamsWithStats
 
diff --git a/src/logdensityfunction.jl b/src/logdensityfunction.jl
index 65eab448e..bcdd0bb25 100644
--- a/src/logdensityfunction.jl
+++ b/src/logdensityfunction.jl
@@ -193,21 +193,21 @@ end
 # LogDensityProblems.jl interface #
 ###################################
 """
-    fast_ldf_accs(getlogdensity::Function)
+    ldf_accs(getlogdensity::Function)
 
 Determine which accumulators are needed for fast evaluation with the given
 `getlogdensity` function.
 """
-fast_ldf_accs(::Function) = default_accumulators()
-fast_ldf_accs(::typeof(getlogjoint_internal)) = default_accumulators()
-function fast_ldf_accs(::typeof(getlogjoint))
+ldf_accs(::Function) = default_accumulators()
+ldf_accs(::typeof(getlogjoint_internal)) = default_accumulators()
+function ldf_accs(::typeof(getlogjoint))
     return AccumulatorTuple((LogPriorAccumulator(), LogLikelihoodAccumulator()))
 end
-function fast_ldf_accs(::typeof(getlogprior_internal))
+function ldf_accs(::typeof(getlogprior_internal))
     return AccumulatorTuple((LogPriorAccumulator(), LogJacobianAccumulator()))
 end
-fast_ldf_accs(::typeof(getlogprior)) = AccumulatorTuple((LogPriorAccumulator(),))
-fast_ldf_accs(::typeof(getloglikelihood)) = AccumulatorTuple((LogLikelihoodAccumulator(),))
+ldf_accs(::typeof(getlogprior)) = AccumulatorTuple((LogPriorAccumulator(),))
+ldf_accs(::typeof(getloglikelihood)) = AccumulatorTuple((LogLikelihoodAccumulator(),))
 
 struct LogDensityAt{M<:Model,F<:Function,N<:NamedTuple}
     model::M
@@ -219,7 +219,7 @@ function (f::LogDensityAt)(params::AbstractVector{<:Real})
     strategy = InitFromParams(
         VectorWithRanges(f.iden_varname_ranges, f.varname_ranges, params), nothing
     )
-    accs = fast_ldf_accs(f.getlogdensity)
+    accs = ldf_accs(f.getlogdensity)
     _, vi = DynamicPPL.init!!(f.model, OnlyAccsVarInfo(accs), strategy)
     return f.getlogdensity(vi)
 end
diff --git a/src/model.jl b/src/model.jl
index 9029318b1..7d5bbf2fb 100644
--- a/src/model.jl
+++ b/src/model.jl
@@ -1181,12 +1181,15 @@ julia> returned(model, Dict{VarName,Float64}(@varname(m) => 2.0))
 ```
 """
 function returned(model::Model, parameters::Union{NamedTuple,AbstractDict{<:VarName}})
-    vi = DynamicPPL.setaccs!!(VarInfo(), ())
     # Note: we can't use `fix(model, parameters)` because
     # https://github.com/TuringLang/DynamicPPL.jl/issues/1097
-    # Use `nothing` as the fallback to ensure that any missing parameters cause an error
-    ctx = InitContext(Random.default_rng(), InitFromParams(parameters, nothing))
-    new_model = setleafcontext(model, ctx)
-    # We can't use new_model() because that overwrites it with an InitContext of its own.
-    return first(evaluate!!(new_model, vi))
+    return first(
+        init!!(
+            model,
+            DynamicPPL.OnlyAccsVarInfo(DynamicPPL.AccumulatorTuple()),
+            # Use `nothing` as the fallback to ensure that any missing parameters cause an
+            # error
+            InitFromParams(parameters, nothing),
+        ),
+    )
 end