diff --git a/base/random/generation.jl b/base/random/generation.jl
index 17a8f02a2017b..29b0b4891ce93 100644
--- a/base/random/generation.jl
+++ b/base/random/generation.jl
@@ -244,32 +244,38 @@ rand(rng::AbstractRNG, sp::SamplerSimple{<:AbstractArray,<:Sampler}) =
     @inbounds return sp[][rand(rng, sp.data)]
 
 
-## random values from Dict, Set, BitSet
+## random values from Dict
 
-for x in (1, Inf) # eval because of ambiguity otherwise
-    for T in (Dict, Set, BitSet)
-        @eval Sampler(::AbstractRNG, t::$T, ::Val{$x}) = SamplerTrivial(t)
-    end
+function Sampler(rng::AbstractRNG, t::Dict, ::Repetition)
+    isempty(t) && throw(ArgumentError("collection must be non-empty"))
+    # we use Val(Inf) below as rand is called repeatedly internally
+    # even for generating only one random value from t
+    SamplerSimple(t, Sampler(rng, linearindices(t.slots), Val(Inf)))
 end
 
-function rand(rng::AbstractRNG, sp::SamplerTrivial{<:Dict})
-    isempty(sp[]) && throw(ArgumentError("collection must be non-empty"))
-    rsp = Sampler(rng, 1:length(sp[].slots))
+function rand(rng::AbstractRNG, sp::SamplerSimple{<:Dict,<:Sampler})
     while true
-        i = rand(rng, rsp)
+        i = rand(rng, sp.data)
         Base.isslotfilled(sp[], i) && @inbounds return (sp[].keys[i] => sp[].vals[i])
     end
 end
 
-rand(rng::AbstractRNG, sp::SamplerTrivial{<:Set}) = rand(rng, sp[].dict).first
+## random values from Set
+
+Sampler(rng::AbstractRNG, t::Set, n::Repetition) = SamplerTag{Set}(Sampler(rng, t.dict, n))
+
+rand(rng::AbstractRNG, sp::SamplerTag{Set,<:Sampler}) = rand(rng, sp.data).first
 
-function rand(rng::AbstractRNG, sp::SamplerTrivial{BitSet})
-    isempty(sp[]) && throw(ArgumentError("collection must be non-empty"))
-    # sp[] can be empty while sp[].bits is not, so we cannot rely on the
-    # length check in Sampler below
-    rsp = Sampler(rng, 1:length(sp[].bits))
+## random values from BitSet
+
+function Sampler(rng::AbstractRNG, t::BitSet, n::Repetition)
+    isempty(t) && throw(ArgumentError("collection must be non-empty"))
+    SamplerSimple(t, Sampler(rng, linearindices(t.bits), Val(Inf)))
+end
+
+function rand(rng::AbstractRNG, sp::SamplerSimple{BitSet,<:Sampler})
     while true
-        n = rand(rng, rsp)
+        n = rand(rng, sp.data)
         @inbounds b = sp[].bits[n]
         b && return n
     end
@@ -277,12 +283,16 @@ end
 
 ## random values from Associative/AbstractSet
 
-# avoid linear complexity for repeated calls
+# we defer to _Sampler to avoid ambiguities with a call like Sampler(rng, Set(1), Val(1))
 Sampler(rng::AbstractRNG, t::Union{Associative,AbstractSet}, n::Repetition) =
+    _Sampler(rng, t, n)
+
+# avoid linear complexity for repeated calls
+_Sampler(rng::AbstractRNG, t::Union{Associative,AbstractSet}, n::Val{Inf}) =
     Sampler(rng, collect(t), n)
 
 # when generating only one element, avoid the call to collect
-Sampler(::AbstractRNG, t::Union{Associative,AbstractSet}, ::Val{1}) =
+_Sampler(::AbstractRNG, t::Union{Associative,AbstractSet}, ::Val{1}) =
     SamplerTrivial(t)
 
 function nth(iter, n::Integer)::eltype(iter)
@@ -299,22 +309,22 @@ rand(rng::AbstractRNG, sp::SamplerTrivial{<:Union{Associative,AbstractSet}}) =
 
 # we use collect(str), which is most of the time more efficient than specialized methods
 # (except maybe for very small arrays)
-Sampler(rng::AbstractRNG, str::AbstractString, n::Repetition) = Sampler(rng, collect(str), n)
+Sampler(rng::AbstractRNG, str::AbstractString, n::Val{Inf}) = Sampler(rng, collect(str), n)
 
 # when generating only one char from a string, the specialized method below
 # is usually more efficient
-Sampler(::AbstractRNG, str::AbstractString, ::Val{1}) = SamplerTrivial(str)
+Sampler(rng::AbstractRNG, str::AbstractString, ::Val{1}) =
+    SamplerSimple(str, Sampler(rng, 1:_endof(str), Val(Inf)))
 
 isvalid_unsafe(s::String, i) = !Base.is_valid_continuation(Base.@gc_preserve s unsafe_load(pointer(s), i))
 isvalid_unsafe(s::AbstractString, i) = isvalid(s, i)
 _endof(s::String) = sizeof(s)
 _endof(s::AbstractString) = endof(s)
 
-function rand(rng::AbstractRNG, sp::SamplerTrivial{<:AbstractString})::Char
+function rand(rng::AbstractRNG, sp::SamplerSimple{<:AbstractString,<:Sampler})::Char
     str = sp[]
-    sp_pos = Sampler(rng, 1:_endof(str))
     while true
-        pos = rand(rng, sp_pos)
+        pos = rand(rng, sp.data)
         isvalid_unsafe(str, pos) && return str[pos]
     end
 end
diff --git a/base/random/random.jl b/base/random/random.jl
index 47cc0b89c7dd4..fe082fdd495d7 100644
--- a/base/random/random.jl
+++ b/base/random/random.jl
@@ -93,6 +93,12 @@ end
 
 Base.getindex(sp::SamplerSimple) = sp.self
 
+# simple sampler carrying a (type) tag T and data
+struct SamplerTag{T,S} <: Sampler
+    data::S
+    SamplerTag{T}(s::S) where {T,S} = new{T,S}(s)
+end
+
 
 ### machinery for generation with Sampler