diff --git a/base/random.jl b/base/random.jl
index dd49d7424fbe7..4a047f01ce673 100644
--- a/base/random.jl
+++ b/base/random.jl
@@ -264,10 +264,6 @@ Pick a random element or array of random elements from the set of values specifi
 
 `S` defaults to [`Float64`](@ref).
 
-Note that the complexity of `rand(rng, s::AbstractString)` is linear
-in the length of `s` if `s` is not of type `String`. If called more
-than a few times, you should use `rand(rng, collect(s))` instead.
-
 # Examples
 
 ```julia-repl
@@ -691,32 +687,27 @@ rand(rng::AbstractRNG, r::AbstractArray, dims::Int...) = rand(rng, r, dims)
 
 # rand from a string
 
-rand(rng::AbstractRNG, s::AbstractString) = rand_iter(rng, s, Base.iteratorsize(s))
-rand(s::AbstractString) = rand(GLOBAL_RNG, s)
-
-## optimization for String
-
 isvalid_unsafe(s::String, i) = !Base.is_valid_continuation(unsafe_load(pointer(s), i))
 
-function rand(rng::AbstractRNG, s::String)
-    rg = RangeGenerator(1:s.len)
+function rand(rng::AbstractRNG, s::String)::Char
+    g = RangeGenerator(1:s.len)
     while true
-        pos = rand(rng, rg)
+        pos = rand(rng, g)
         isvalid_unsafe(s, pos) && return s[pos]
     end
 end
 
-## rand from an iterator
-
-rand_iter(rng, s, ::Base.IteratorSize) = throw(ArgumentError("iterator must have a known length"))
-
-function rand_iter(rng::AbstractRNG, s, ::Union{Base.HasShape,Base.HasLength})::eltype(s)
-    pos = rand(rng, 1:length(s))
-    for (i, c) in enumerate(s)
-        i == pos && return c
+function rand(rng::AbstractRNG, s::AbstractString)::Char
+    g = RangeGenerator(1:endof(s))
+    while true
+        try # the generic `isvalid` includes an equivalent try/catch statement
+            return s[rand(rng, g)]
+        end
     end
 end
 
+rand(s::AbstractString) = rand(GLOBAL_RNG, s)
+
 ## rand from a string for arrays
 # we use collect(str), which is most of the time more efficient than specialized methods
 # (except maybe for very small arrays)