diff --git a/src/bin/pg_probackup/pg_lzcompress.cpp b/src/bin/pg_probackup/pg_lzcompress.cpp
index 32d01f5b797613bea301c00047013c6ef8e91ba9..bd3571a57c9ccabdcec536617587dc127b960e2b 100644
--- a/src/bin/pg_probackup/pg_lzcompress.cpp
+++ b/src/bin/pg_probackup/pg_lzcompress.cpp
@@ -252,8 +252,8 @@ const PGLZ_Strategy *const PGLZ_strategy_always = &strategy_always_data;
  * Statically allocated work arrays for history
  * ----------
  */
-static int16 hist_start[PGLZ_MAX_HISTORY_LISTS];
-static PGLZ_HistEntry hist_entries[PGLZ_HISTORY_SIZE + 1];
+static THR_LOCAL int16 hist_start[PGLZ_MAX_HISTORY_LISTS];
+static THR_LOCAL PGLZ_HistEntry hist_entries[PGLZ_HISTORY_SIZE + 1];
 
 /*
  * Element 0 in hist_entries is unused, and means 'invalid'. Likewise,
diff --git a/src/bin/pg_probackup/pg_probackup.cpp b/src/bin/pg_probackup/pg_probackup.cpp
index f0275344cfcf514d7a485584e462782541b41192..64da319438c09ebd382f283b6bc112bea9adcad9 100644
--- a/src/bin/pg_probackup/pg_probackup.cpp
+++ b/src/bin/pg_probackup/pg_probackup.cpp
@@ -923,10 +923,7 @@ compress_init(void)
 #ifndef HAVE_LIBZ
         if (instance_config.compress_alg == ZLIB_COMPRESS)
             elog(ERROR, "This build does not support zlib compression");
-        else
 #endif
-        if (instance_config.compress_alg == PGLZ_COMPRESS && num_threads > 1)
-            elog(ERROR, "Multithread backup does not support pglz compression");
     }
 }