diff --git a/src/noop.jl b/src/noop.jl
index d5b511c7..1a3e65f4 100644
--- a/src/noop.jl
+++ b/src/noop.jl
@@ -167,7 +167,7 @@ function fillbuffer(stream::NoopStream; eager::Bool = false)
     end
     nfilled::Int = 0
     while ((!eager && buffersize(buffer) == 0) || (eager && makemargin!(buffer, 0, eager = true) > 0)) && !eof(stream.stream)
-        makemargin!(buffer, 1)
+        makemargin!(buffer, max(1, div(length(buffer), 2)))
         nfilled += readdata!(stream.stream, buffer)
     end
     buffer.transcoded += nfilled
diff --git a/src/stream.jl b/src/stream.jl
index ade7a058..fb4bc88d 100644
--- a/src/stream.jl
+++ b/src/stream.jl
@@ -575,7 +575,7 @@ function fillbuffer(stream::TranscodingStream; eager::Bool = false)
             end
             callstartproc(stream, :read)
         end
-        makemargin!(buffer2, 1)
+        makemargin!(buffer2, max(1, div(length(buffer2), 2)))
         readdata!(stream.stream, buffer2)
         _, Δout = callprocess(stream, buffer2, buffer1)
         nfilled += Δout