diff --git a/src/backend/commands/copy.c b/src/backend/commands/copy.c
index 3a66cb5025..78f7db07f0 100644
--- a/src/backend/commands/copy.c
+++ b/src/backend/commands/copy.c
@@ -42,6 +42,7 @@
 #include "parser/parse_relation.h"
 #include "port/pg_bswap.h"
 #include "rewrite/rewriteHandler.h"
+#include "storage/bufmgr.h"
 #include "storage/fd.h"
 #include "tcop/tcopprot.h"
 #include "utils/builtins.h"
@@ -2404,7 +2405,16 @@ CopyFrom(CopyState cstate)
 		cstate->rel->rd_newRelfilenodeSubid != InvalidSubTransactionId)
 	{
 		hi_options |= HEAP_INSERT_SKIP_FSM;
-		if (!XLogIsNeeded())
+
+		/*
+		 * Skip writing WAL if there have been no actions that write an init
+		 * block for any of the buffers that will be touched during COPY.
+		 * Since there is no way of knowing at present which ones these are,
+		 * we must use a simple but effective heuristic to ensure safety of
+		 * the COPY operation for all cases, which is in this case to check
+		 * that the relation copied to has zero blocks.
+		 */
+		if (!XLogIsNeeded() && RelationGetNumberOfBlocks(cstate->rel) == 0)
 			hi_options |= HEAP_INSERT_SKIP_WAL;
 	}
 
diff --git a/src/backend/commands/tablecmds.c b/src/backend/commands/tablecmds.c
index 7c0cf0d7ee..90fe27fbf9 100644
--- a/src/backend/commands/tablecmds.c
+++ b/src/backend/commands/tablecmds.c
@@ -1562,10 +1562,15 @@ ExecuteTruncateGuts(List *explicit_rels, List *relids, List *relids_logged,
 		 * the table was either created in the current (sub)transaction or has
 		 * a new relfilenode in the current (sub)transaction, then we can just
 		 * truncate it in-place, because a rollback would cause the whole
-		 * table or the current physical file to be thrown away anyway.
+		 * table or the current physical file to be thrown away anyway.  This
+		 * optimization is not safe with wal_level = minimal as there is no
+		 * actual way to know which are the blocks that could have been
+		 * touched by another operation done within this same transaction, be
+		 * it INSERT or COPY.
 		 */
-		if (rel->rd_createSubid == mySubid ||
-			rel->rd_newRelfilenodeSubid == mySubid)
+		if (XLogIsNeeded() &&
+			(rel->rd_createSubid == mySubid ||
+			 rel->rd_newRelfilenodeSubid == mySubid))
 		{
 			/* Immediate, non-rollbackable truncation is OK */
 			heap_truncate_one_rel(rel);
diff --git a/src/test/recovery/t/015_wal_optimize.pl b/src/test/recovery/t/015_wal_optimize.pl
new file mode 100644
index 0000000000..98a410b125
--- /dev/null
+++ b/src/test/recovery/t/015_wal_optimize.pl
@@ -0,0 +1,120 @@
+# Test WAL replay for optimized TRUNCATE and COPY records
+#
+# WAL truncation is optimized in some cases with TRUNCATE and COPY queries
+# which sometimes interact badly with the other optimizations in line with
+# several setting values of wal_level, particularly when using "minimal" or
+# "replica".  The optimization may be enabled or disabled depending on the
+# scenarios dealt here, and should never result in any type of failures or
+# data loss.
+use strict;
+use warnings;
+
+use PostgresNode;
+use TestLib;
+use Test::More tests => 10;
+
+# Wrapper routine tunable for wal_level.
+sub run_wal_optimize
+{
+	my $wal_level = shift;
+
+	# Primary needs to have wal_level = minimal here
+	my $node = get_new_node("node_$wal_level");
+	$node->init;
+	$node->append_conf('postgresql.conf', qq(
+wal_level = $wal_level
+));
+	$node->start;
+
+	# Test direct truncation optimization.  No tuples
+	$node->safe_psql('postgres', "
+		BEGIN;
+		CREATE TABLE test1 (id serial PRIMARY KEY);
+		TRUNCATE test1;
+		COMMIT;");
+
+	$node->stop('immediate');
+	$node->start;
+
+	my $result = $node->safe_psql('postgres', "SELECT count(*) FROM test1;");
+	is($result, qq(0),
+	   "wal_level = $wal_level, optimized truncation with empty table");
+
+	# Test truncation with inserted tuples within the same transaction.
+	# Tuples inserted after the truncation should be seen.
+	$node->safe_psql('postgres', "
+		BEGIN;
+		CREATE TABLE test2 (id serial PRIMARY KEY);
+		INSERT INTO test2 VALUES (DEFAULT);
+		TRUNCATE test2;
+		INSERT INTO test2 VALUES (DEFAULT);
+		COMMIT;");
+
+	$node->stop('immediate');
+	$node->start;
+
+	$result = $node->safe_psql('postgres', "SELECT count(*) FROM test2;");
+	is($result, qq(1),
+	   "wal_level = $wal_level, optimized truncation with inserted table");
+
+	# Data file for COPY query in follow-up tests.
+	my $basedir = $node->basedir;
+	my $copy_file = "$basedir/copy_data.txt";
+	TestLib::append_to_file($copy_file, qq(20000,30000
+20001,30001
+20002,30002));
+
+	# Test truncation with inserted tuples using COPY.  Tuples copied after the
+	# truncation should be seen.
+	$node->safe_psql('postgres', "
+		BEGIN;
+		CREATE TABLE test3 (id serial PRIMARY KEY, id2 int);
+		INSERT INTO test3 (id, id2) VALUES (DEFAULT, generate_series(1,10000));
+		TRUNCATE test3;
+		COPY test3 FROM '$copy_file' DELIMITER ',';
+		COMMIT;");
+	$node->stop('immediate');
+	$node->start;
+	$result = $node->safe_psql('postgres', "SELECT count(*) FROM test3;");
+	is($result, qq(3),
+	   "wal_level = $wal_level, optimized truncation with copied table");
+
+	# Test truncation with inserted tuples using both INSERT and COPY. Tuples
+	# inserted after the truncation should be seen.
+	$node->safe_psql('postgres', "
+		BEGIN;
+		CREATE TABLE test4 (id serial PRIMARY KEY, id2 int);
+		INSERT INTO test4 (id, id2) VALUES (DEFAULT, generate_series(1,10000));
+		TRUNCATE test4;
+		INSERT INTO test4 (id, id2) VALUES (DEFAULT, 10000);
+		COPY test4 FROM '$copy_file' DELIMITER ',';
+		INSERT INTO test4 (id, id2) VALUES (DEFAULT, 10000);
+		COMMIT;");
+
+	$node->stop('immediate');
+	$node->start;
+	$result = $node->safe_psql('postgres', "SELECT count(*) FROM test4;");
+	is($result, qq(5),
+	   "wal_level = $wal_level, optimized truncation with inserted/copied table");
+
+	# Test consistency of COPY with INSERT for table created in the same
+	# transaction.
+	$node->safe_psql('postgres', "
+		BEGIN;
+		CREATE TABLE test5 (id serial PRIMARY KEY, id2 int);
+		INSERT INTO test5 VALUES (DEFAULT, 1);
+		COPY test5 FROM '$copy_file' DELIMITER ',';
+		COMMIT;");
+	$node->stop('immediate');
+	$node->start;
+	$result = $node->safe_psql('postgres', "SELECT count(*) FROM test5;");
+	is($result, qq(4),
+	   "wal_level = $wal_level, replay of optimized copy with inserted table");
+
+	$node->teardown_node;
+	$node->clean_node;
+}
+
+# Run same test suite for multiple wal_level values.
+run_wal_optimize("minimal");
+run_wal_optimize("replica");