diff --git a/lib/restclient/request.rb b/lib/restclient/request.rb
index f011c91..86a3c6b 100644
--- a/lib/restclient/request.rb
+++ b/lib/restclient/request.rb
@@ -557,7 +557,8 @@ module RestClient
     def transmit uri, req, payload, & block
 
       # We set this to true in the net/http block so that we can distinguish
-      # read_timeout from open_timeout. This isn't needed in Ruby >= 2.0.
+      # read_timeout from open_timeout. Now that we only support Ruby 2.0+,
+      # this is only needed for Timeout exceptions thrown outside of Net::HTTP.
       established_connection = false
 
       setup_credentials req
@@ -641,18 +642,12 @@ module RestClient
       end
     rescue EOFError
       raise RestClient::ServerBrokeConnection
+    rescue Net::OpenTimeout => err
+      raise RestClient::Exceptions::OpenTimeout.new(nil, err)
+    rescue Net::ReadTimeout => err
+      raise RestClient::Exceptions::ReadTimeout.new(nil, err)
     rescue Timeout::Error, Errno::ETIMEDOUT => err
-      # Net::HTTP has OpenTimeout, ReadTimeout in Ruby >= 2.0
-      if defined?(Net::OpenTimeout)
-        case err
-        when Net::OpenTimeout
-          raise RestClient::Exceptions::OpenTimeout.new(nil, err)
-        when Net::ReadTimeout
-          raise RestClient::Exceptions::ReadTimeout.new(nil, err)
-        end
-      end
-
-      # compatibility for Ruby 1.9.3, handling for non-Net::HTTP timeouts
+      # handling for non-Net::HTTP timeouts
       if established_connection
         raise RestClient::Exceptions::ReadTimeout.new(nil, err)
       else