diff --git a/.unreleased/pr_7789 b/.unreleased/pr_7789
new file mode 100644
index 00000000000..b71fdafde10
--- /dev/null
+++ b/.unreleased/pr_7789
@@ -0,0 +1,2 @@
+Implements: #7789 Do not recompress segmentwise when default order by is empty
+Fixes: #7748 Crash in the segmentwise recompression
diff --git a/tsl/src/compression/api.c b/tsl/src/compression/api.c
index 7f61b6865af..6b8d89206ba 100644
--- a/tsl/src/compression/api.c
+++ b/tsl/src/compression/api.c
@@ -940,12 +940,14 @@ tsl_compress_chunk_wrapper(Chunk *chunk, bool if_not_compressed, bool recompress
 
 	if (ts_chunk_is_compressed(chunk))
 	{
+		CompressionSettings *chunk_settings = ts_compression_settings_get(chunk->table_id);
+		bool valid_orderby_settings = chunk_settings->fd.orderby;
 		if (recompress)
 		{
 			CompressionSettings *ht_settings = ts_compression_settings_get(chunk->hypertable_relid);
-			CompressionSettings *chunk_settings = ts_compression_settings_get(chunk->table_id);
 
-			if (!ts_compression_settings_equal(ht_settings, chunk_settings))
+			if (!valid_orderby_settings ||
+				!ts_compression_settings_equal(ht_settings, chunk_settings))
 			{
 				decompress_chunk_impl(chunk, false);
 				compress_chunk_impl(chunk->hypertable_relid, chunk->table_id);
@@ -962,17 +964,21 @@ tsl_compress_chunk_wrapper(Chunk *chunk, bool if_not_compressed, bool recompress
 			return uncompressed_chunk_id;
 		}
 
-		if (ts_guc_enable_segmentwise_recompression && ts_chunk_is_partial(chunk) &&
-			get_compressed_chunk_index_for_recompression(chunk))
+		if (ts_guc_enable_segmentwise_recompression && valid_orderby_settings &&
+			ts_chunk_is_partial(chunk) && get_compressed_chunk_index_for_recompression(chunk))
 		{
 			uncompressed_chunk_id = recompress_chunk_segmentwise_impl(chunk);
 		}
 		else
 		{
-			if (!ts_guc_enable_segmentwise_recompression)
+			if (!ts_guc_enable_segmentwise_recompression || !valid_orderby_settings)
 				elog(NOTICE,
-					 "segmentwise recompression is disabled, performing full recompression on "
+					 "segmentwise recompression is disabled%s, performing full "
+					 "recompression on "
 					 "chunk \"%s.%s\"",
+					 (ts_guc_enable_segmentwise_recompression && !valid_orderby_settings ?
+						  " due to no order by" :
+						  ""),
 					 NameStr(chunk->fd.schema_name),
 					 NameStr(chunk->fd.table_name));
 			decompress_chunk_impl(chunk, false);
diff --git a/tsl/src/compression/create.c b/tsl/src/compression/create.c
index be722ec035f..f9fc867bd51 100644
--- a/tsl/src/compression/create.c
+++ b/tsl/src/compression/create.c
@@ -1142,10 +1142,16 @@ compression_setting_orderby_get_default(Hypertable *ht, ArrayType *segmentby)
 	else
 		orderby = "";
 
-	elog(NOTICE,
-		 "default order by for hypertable \"%s\" is set to \"%s\"",
-		 get_rel_name(ht->main_table_relid),
-		 orderby);
+	if (*orderby == '\0')
+		ereport(NOTICE,
+				(errmsg("default order by for hypertable \"%s\" is set to \"\"",
+						get_rel_name(ht->main_table_relid))),
+				errdetail("Segmentwise recompression will be disabled"));
+	else
+		elog(NOTICE,
+			 "default order by for hypertable \"%s\" is set to \"%s\"",
+			 get_rel_name(ht->main_table_relid),
+			 orderby);
 
 	elog(LOG_SERVER_ONLY,
 		 "order_by default: hypertable=\"%s\" clauses=\"%s\" function=\"%s.%s\" confidence=%d",
diff --git a/tsl/src/compression/recompress.c b/tsl/src/compression/recompress.c
index a268e74d09a..609d57a59d1 100644
--- a/tsl/src/compression/recompress.c
+++ b/tsl/src/compression/recompress.c
@@ -18,6 +18,7 @@
 #include "compression.h"
 #include "compression_dml.h"
 #include "create.h"
+#include "debug_assert.h"
 #include "guc.h"
 #include "hypercore/hypercore_handler.h"
 #include "hypercore/utils.h"
@@ -83,6 +84,15 @@ tsl_recompress_chunk_segmentwise(PG_FUNCTION_ARGS)
 							"enable it by first setting "
 							"timescaledb.enable_segmentwise_recompression to on")));
 		}
+		CompressionSettings *settings = ts_compression_settings_get(uncompressed_chunk_id);
+		if (!settings->fd.orderby)
+		{
+			ereport(ERROR,
+					(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+					 errmsg("segmentwise recompression cannot be applied for "
+							"compression with no "
+							"order by")));
+		}
 		uncompressed_chunk_id = recompress_chunk_segmentwise_impl(chunk);
 	}
 
@@ -112,6 +122,10 @@ recompress_chunk_segmentwise_impl(Chunk *uncompressed_chunk)
 	Chunk *compressed_chunk = ts_chunk_get_by_id(uncompressed_chunk->fd.compressed_chunk_id, true);
 	CompressionSettings *settings = ts_compression_settings_get(uncompressed_chunk->table_id);
 
+	/* We should not do segment-wise recompression with empty orderby, see #7748
+	 */
+	Ensure(settings->fd.orderby, "empty order by, cannot recompress segmentwise");
+
 	/* new status after recompress should simply be compressed (1)
 	 * It is ok to update this early on in the transaction as it keeps a lock
 	 * on the updated tuple in the CHUNK table potentially preventing other transaction
diff --git a/tsl/test/expected/recompress_chunk_segmentwise.out b/tsl/test/expected/recompress_chunk_segmentwise.out
index 9f42ea8993b..1e327ca2f3b 100644
--- a/tsl/test/expected/recompress_chunk_segmentwise.out
+++ b/tsl/test/expected/recompress_chunk_segmentwise.out
@@ -647,13 +647,51 @@ INFO:  Using index "compress_hyper_19_20_chunk__ts_meta_min_1__ts_meta_max_1_idx
  _timescaledb_internal._hyper_18_19_chunk
 (1 row)
 
+-- Test behaviour when default order by is empty: should not segmentwise-recompress in this case
+CREATE TABLE no_oby(ts int, c1 int);
+SELECT create_hypertable('no_oby','ts');
+NOTICE:  adding not-null constraint to column "ts"
+  create_hypertable   
+----------------------
+ (20,public,no_oby,t)
+(1 row)
+
+\set VERBOSITY default
+ALTER TABLE no_oby SET (timescaledb.compress, timescaledb.compress_segmentby = 'ts');
+NOTICE:  default order by for hypertable "no_oby" is set to ""
+DETAIL:  Segmentwise recompression will be disabled
+\set VERBOSITY terse
+INSERT INTO no_oby (ts,c1) VALUES (6,6);
+SELECT show_chunks as chunk_to_compress FROM show_chunks('no_oby') LIMIT 1 \gset
+SELECT compress_chunk(:'chunk_to_compress');
+INFO:  using tuplesort to scan rows from "_hyper_20_21_chunk" for compression
+              compress_chunk              
+------------------------------------------
+ _timescaledb_internal._hyper_20_21_chunk
+(1 row)
+
+INSERT INTO no_oby (ts,c1) VALUES (7,7);
+-- Direct segmentwise-recompress request: throw an error
+\set ON_ERROR_STOP 0
+SELECT _timescaledb_functions.recompress_chunk_segmentwise(:'chunk_to_compress');
+ERROR:  segmentwise recompression cannot be applied for compression with no order by
+\set ON_ERROR_STOP 1
+-- Compress wrapper: do full recompress instead of by segment
+SELECT compress_chunk(:'chunk_to_compress');
+NOTICE:  segmentwise recompression is disabled due to no order by, performing full recompression on chunk "_timescaledb_internal._hyper_20_21_chunk"
+INFO:  using tuplesort to scan rows from "_hyper_20_21_chunk" for compression
+              compress_chunk              
+------------------------------------------
+ _timescaledb_internal._hyper_20_21_chunk
+(1 row)
+
 RESET timescaledb.debug_compression_path_info;
 --- Test behaviour when enable_segmentwise_recompression GUC if OFF
 CREATE TABLE guc_test(time timestamptz not null, a int, b int, c int);
 SELECT create_hypertable('guc_test', by_range('time', INTERVAL '1 day'));
  create_hypertable 
 -------------------
- (20,t)
+ (22,t)
 (1 row)
 
 ALTER TABLE guc_test set (timescaledb.compress, timescaledb.compress_segmentby = 'a, b');
@@ -663,7 +701,7 @@ SELECT show_chunks as chunk_to_compress FROM show_chunks('guc_test') LIMIT 1 \gs
 SELECT compress_chunk(:'chunk_to_compress');
               compress_chunk              
 ------------------------------------------
- _timescaledb_internal._hyper_20_21_chunk
+ _timescaledb_internal._hyper_22_24_chunk
 (1 row)
 
 INSERT INTO guc_test VALUES ('2024-10-30 14:14:00.501519-06'::timestamptz, 1, 1, 2);
@@ -675,9 +713,9 @@ ERROR:  segmentwise recompression functionality disabled, enable it by first set
 \set ON_ERROR_STOP 1
 -- When GUC is OFF, entire chunk should be fully uncompressed and compressed instead
 SELECT compress_chunk(:'chunk_to_compress');
-NOTICE:  segmentwise recompression is disabled, performing full recompression on chunk "_timescaledb_internal._hyper_20_21_chunk"
+NOTICE:  segmentwise recompression is disabled, performing full recompression on chunk "_timescaledb_internal._hyper_22_24_chunk"
               compress_chunk              
 ------------------------------------------
- _timescaledb_internal._hyper_20_21_chunk
+ _timescaledb_internal._hyper_22_24_chunk
 (1 row)
 
diff --git a/tsl/test/sql/recompress_chunk_segmentwise.sql b/tsl/test/sql/recompress_chunk_segmentwise.sql
index 9cd179a50c8..22521831cb2 100644
--- a/tsl/test/sql/recompress_chunk_segmentwise.sql
+++ b/tsl/test/sql/recompress_chunk_segmentwise.sql
@@ -307,6 +307,25 @@ INSERT INTO noseg VALUES ('2025-01-24 10:54:27.323421-07'::timestamptz, 1, 1, 2)
 -- should recompress chunk using the default index
 SELECT compress_chunk(:'chunk_to_compress');
 
+-- Test behaviour when default order by is empty: should not segmentwise-recompress in this case
+CREATE TABLE no_oby(ts int, c1 int);
+SELECT create_hypertable('no_oby','ts');
+\set VERBOSITY default
+ALTER TABLE no_oby SET (timescaledb.compress, timescaledb.compress_segmentby = 'ts');
+\set VERBOSITY terse
+
+INSERT INTO no_oby (ts,c1) VALUES (6,6);
+SELECT show_chunks as chunk_to_compress FROM show_chunks('no_oby') LIMIT 1 \gset
+SELECT compress_chunk(:'chunk_to_compress');
+
+INSERT INTO no_oby (ts,c1) VALUES (7,7);
+-- Direct segmentwise-recompress request: throw an error
+\set ON_ERROR_STOP 0
+SELECT _timescaledb_functions.recompress_chunk_segmentwise(:'chunk_to_compress');
+\set ON_ERROR_STOP 1
+-- Compress wrapper: do full recompress instead of by segment
+SELECT compress_chunk(:'chunk_to_compress');
+
 RESET timescaledb.debug_compression_path_info;
 
 --- Test behaviour when enable_segmentwise_recompression GUC if OFF