diff --git a/src/Parser.jl b/src/Parser.jl
index 5b1f9d7..0a4eaf1 100644
--- a/src/Parser.jl
+++ b/src/Parser.jl
@@ -105,7 +105,7 @@ Return `true` if there is a current byte, and `false` if all bytes have been
 exausted.
 """
 @inline hasmore(ps::MemoryParserState) = ps.s ≤ length(ps)
-@inline hasmore(ps::StreamingParserState) = true  # no more now ≠ no more ever
+@inline hasmore(ps::StreamingParserState) = !ps.used || !eof(ps.io)
 
 """
 Remove as many whitespace bytes as possible from the `ParserState` starting from
diff --git a/test/runtests.jl b/test/runtests.jl
index d585154..0d950d0 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -42,6 +42,10 @@ include("json-samples.jl")
         @test JSON.parse("1") == 1
         @test JSON.parse("1.5") == 1.5
         @test JSON.parse("[true]") == [true]
+
+        # test for parsing single values in streams
+        @test JSON.parse(IOBuffer("123")) == 123
+        @test JSON.parse(IOBuffer("1.5")) == 1.5
     end
 end