Refactorings and renamings related to compression.

Also added levels to the channel args options.
diff --git a/src/cpp/client/client_context.cc b/src/cpp/client/client_context.cc
index 32c7794..d3e5ce0 100644
--- a/src/cpp/client/client_context.cc
+++ b/src/cpp/client/client_context.cc
@@ -33,15 +33,14 @@
 
 #include <grpc++/client_context.h>
 
-#include <grpc++/security/credentials.h>
-#include <grpc++/server_context.h>
-#include <grpc++/support/time.h>
 #include <grpc/compression.h>
 #include <grpc/grpc.h>
 #include <grpc/support/alloc.h>
 #include <grpc/support/string_util.h>
 
-#include "src/core/lib/channel/compress_filter.h"
+#include <grpc++/security/credentials.h>
+#include <grpc++/server_context.h>
+#include <grpc++/support/time.h>
 
 namespace grpc {
 
@@ -112,7 +111,7 @@
     abort();
   }
   GPR_ASSERT(algorithm_name != nullptr);
-  AddMetadata(GRPC_COMPRESS_REQUEST_ALGORITHM_KEY, algorithm_name);
+  AddMetadata(GRPC_COMPRESSION_REQUEST_ALGORITHM_MD_KEY, algorithm_name);
 }
 
 void ClientContext::TryCancel() {
diff --git a/src/cpp/server/server_builder.cc b/src/cpp/server/server_builder.cc
index 61f0f6a..e6050c3 100644
--- a/src/cpp/server/server_builder.cc
+++ b/src/cpp/server/server_builder.cc
@@ -125,6 +125,13 @@
   }
   args.SetInt(GRPC_COMPRESSION_CHANNEL_ENABLED_ALGORITHMS_BITSET,
               compression_options_.enabled_algorithms_bitset);
+  if (compression_options_.default_level.is_set) {
+    args.SetInt(GRPC_COMPRESSION_CHANNEL_DEFAULT_LEVEL,
+                compression_options_.default_level.level);
+  } else if (compression_options_.default_algorithm.is_set) {
+    args.SetInt(GRPC_COMPRESSION_CHANNEL_DEFAULT_ALGORITHM,
+                compression_options_.default_algorithm.algorithm);
+  }
   std::unique_ptr<Server> server(
       new Server(thread_pool.release(), true, max_message_size_, &args));
   ServerInitializer* initializer = server->initializer();
diff --git a/src/cpp/server/server_context.cc b/src/cpp/server/server_context.cc
index 204fef1..43117fd 100644
--- a/src/cpp/server/server_context.cc
+++ b/src/cpp/server/server_context.cc
@@ -42,7 +42,6 @@
 #include <grpc/support/alloc.h>
 #include <grpc/support/log.h>
 
-#include "src/core/lib/channel/compress_filter.h"
 #include "src/core/lib/surface/call.h"
 
 namespace grpc {
@@ -196,6 +195,9 @@
 }
 
 void ServerContext::set_compression_level(grpc_compression_level level) {
+  // TODO(dgq): get rid of grpc_call_compression_for_level and propagate the
+  // compression level by adding a new argument to
+  // CallOpSendInitialMetadata::SendInitialMetadata.
   const grpc_compression_algorithm algorithm_for_level =
       grpc_call_compression_for_level(call_, level);
   set_compression_algorithm(algorithm_for_level);
@@ -210,7 +212,7 @@
     abort();
   }
   GPR_ASSERT(algorithm_name != NULL);
-  AddInitialMetadata(GRPC_COMPRESS_REQUEST_ALGORITHM_KEY, algorithm_name);
+  AddInitialMetadata(GRPC_COMPRESSION_REQUEST_ALGORITHM_MD_KEY, algorithm_name);
 }
 
 grpc::string ServerContext::peer() const {