diff --git a/src/backend/backup/basebackup.c b/src/backend/backup/basebackup.c
index 5fea86ad0f..b956df072d 100644
--- a/src/backend/backup/basebackup.c
+++ b/src/backend/backup/basebackup.c
@@ -1623,6 +1623,8 @@ sendFile(bbsink *sink, const char *readfilename, const char *tarfilename,
 	{
 		unsigned	magic = INCREMENTAL_MAGIC;
 		size_t		header_bytes_done = 0;
+		char		padding[BLCKSZ];
+		size_t		paddinglen;
 
 		/* Emit header data. */
 		push_to_sink(sink, &checksum_ctx, &header_bytes_done,
@@ -1635,6 +1637,23 @@ sendFile(bbsink *sink, const char *readfilename, const char *tarfilename,
 					 incremental_blocks,
 					 sizeof(BlockNumber) * num_incremental_blocks);
 
+		/*
+		 * Add padding to align header to a multiple of BLCKSZ, but only if
+		 * the incremental file has some blocks. If there are no blocks we
+		 * don't want make the file unnecessarily large, as that might make
+		 * some filesystem optimizations impossible.
+		 */
+		if (num_incremental_blocks > 0)
+		{
+			paddinglen = (BLCKSZ - (header_bytes_done % BLCKSZ));
+
+			memset(padding, 0, paddinglen);
+			bytes_done += paddinglen;
+
+			push_to_sink(sink, &checksum_ctx, &header_bytes_done,
+						 padding, paddinglen);
+		}
+
 		/* Flush out any data still in the buffer so it's again empty. */
 		if (header_bytes_done > 0)
 		{
@@ -1748,6 +1767,13 @@ sendFile(bbsink *sink, const char *readfilename, const char *tarfilename,
 		blkno += cnt / BLCKSZ;
 		bytes_done += cnt;
 
+		/*
+		 * Make sure incremental files with block data are properly aligned
+		 * (header is a multiple of BLCKSZ, blocks are BLCKSZ too).
+		 */
+		Assert(!((incremental_blocks != NULL && num_incremental_blocks > 0) &&
+				 (bytes_done % BLCKSZ != 0)));
+
 		/* Archive the data we just read. */
 		bbsink_archive_contents(sink, cnt);
 
diff --git a/src/backend/backup/basebackup_incremental.c b/src/backend/backup/basebackup_incremental.c
index 2970dfe603..131598bade 100644
--- a/src/backend/backup/basebackup_incremental.c
+++ b/src/backend/backup/basebackup_incremental.c
@@ -928,6 +928,36 @@ GetFileBackupMethod(IncrementalBackupInfo *ib, const char *path,
 	return BACK_UP_FILE_INCREMENTALLY;
 }
 
+/*
+ * Compute the size for a header of an incremental file containing a given
+ * number of blocks. The header is rounded to a multiple of BLCKSZ, but
+ * only if the file will store some block data.
+ */
+extern size_t
+GetIncrementalHeaderSize(unsigned num_blocks_required)
+{
+	size_t		result;
+
+	/* Make sure we're not going to overflow. */
+	Assert(num_blocks_required <= RELSEG_SIZE);
+
+	/*
+	 * Three four byte quantities (magic number, truncation block length,
+	 * block count) followed by block numbers.
+	 */
+	result = 3 * sizeof(uint32) + (sizeof(BlockNumber) * num_blocks_required);
+
+	/*
+	 * Round the header size to a multiple of BLCKSZ - when not a multiple of
+	 * BLCKSZ, add the missing fraction of a block. But do this only if the
+	 * file will store data for some blocks, otherwise keep it small.
+	 */
+	if ((num_blocks_required > 0) && (result % BLCKSZ != 0))
+		result += BLCKSZ - (result % BLCKSZ);
+
+	return result;
+}
+
 /*
  * Compute the size for an incremental file containing a given number of blocks.
  */
@@ -940,11 +970,12 @@ GetIncrementalFileSize(unsigned num_blocks_required)
 	Assert(num_blocks_required <= RELSEG_SIZE);
 
 	/*
-	 * Three four byte quantities (magic number, truncation block length,
-	 * block count) followed by block numbers followed by block contents.
+	 * Header with three four byte quantities (magic number, truncation block
+	 * length, block count) followed by block numbers, rounded to a multiple
+	 * of BLCKSZ (for files with block data), followed by block contents.
 	 */
-	result = 3 * sizeof(uint32);
-	result += (BLCKSZ + sizeof(BlockNumber)) * num_blocks_required;
+	result = GetIncrementalHeaderSize(num_blocks_required);
+	result += BLCKSZ * num_blocks_required;
 
 	return result;
 }
diff --git a/src/bin/pg_combinebackup/reconstruct.c b/src/bin/pg_combinebackup/reconstruct.c
index 41f06bb26b..33c6da02a8 100644
--- a/src/bin/pg_combinebackup/reconstruct.c
+++ b/src/bin/pg_combinebackup/reconstruct.c
@@ -472,6 +472,14 @@ make_incremental_rfile(char *filename)
 		sizeof(rf->truncation_block_length) +
 		sizeof(BlockNumber) * rf->num_blocks;
 
+	/*
+	 * Round header length to a multiple of BLCKSZ, so that blocks contents
+	 * are properly aligned. Only do this when the file actually has data for
+	 * some blocks.
+	 */
+	if ((rf->num_blocks > 0) && ((rf->header_length % BLCKSZ) != 0))
+		rf->header_length += (BLCKSZ - (rf->header_length % BLCKSZ));
+
 	return rf;
 }
 
diff --git a/src/include/backup/basebackup_incremental.h b/src/include/backup/basebackup_incremental.h
index ae5feb4b32..6ba9c9035e 100644
--- a/src/include/backup/basebackup_incremental.h
+++ b/src/include/backup/basebackup_incremental.h
@@ -51,5 +51,6 @@ extern FileBackupMethod GetFileBackupMethod(IncrementalBackupInfo *ib,
 											BlockNumber *relative_block_numbers,
 											unsigned *truncation_block_length);
 extern size_t GetIncrementalFileSize(unsigned num_blocks_required);
+extern size_t GetIncrementalHeaderSize(unsigned num_blocks_required);
 
 #endif