diff --git a/cli/util/upload_bin.go b/cli/util/upload_bin.go
index 4c15c1ebc..1086fe18f 100644
--- a/cli/util/upload_bin.go
+++ b/cli/util/upload_bin.go
@@ -36,8 +36,9 @@ const (
 	// except the most recent one are guaranteed to be completed and don't contain gaps.
 	uploadBatchSize = 10000
 	// Number of objects to search in a batch. If it is larger than uploadBatchSize,
-	// it may lead to many duplicate uploads.
-	searchBatchSize = uploadBatchSize
+	// it may lead to many duplicate uploads. We need to search with EQ filter to
+	//avoid partially-completed SEARCH responses.
+	searchBatchSize = 1
 	// Size of object ID.
 	oidSize = sha256.Size
 )
@@ -214,8 +215,12 @@ func fetchLatestMissingBlockIndex(ctx context.Context, p *pool.Pool, containerID
 
 				prm := client.PrmObjectSearch{}
 				filters := object.NewSearchFilters()
-				filters.AddFilter(attributeKey, fmt.Sprintf("%d", startIndex), object.MatchNumGE)
-				filters.AddFilter(attributeKey, fmt.Sprintf("%d", endIndex), object.MatchNumLT)
+				if endIndex == startIndex+1 {
+					filters.AddFilter(attributeKey, fmt.Sprintf("%d", startIndex), object.MatchStringEqual)
+				} else {
+					filters.AddFilter(attributeKey, fmt.Sprintf("%d", startIndex), object.MatchNumGE)
+					filters.AddFilter(attributeKey, fmt.Sprintf("%d", endIndex), object.MatchNumLT)
+				}
 				prm.SetFilters(filters)
 				var (
 					objectIDs []oid.ID
@@ -527,8 +532,12 @@ func searchObjects(ctx context.Context, p *pool.Pool, containerID cid.ID, accoun
 					if len(additionalFilters) != 0 {
 						filters = additionalFilters[0]
 					}
-					filters.AddFilter(blockAttributeKey, fmt.Sprintf("%d", start), object.MatchNumGE)
-					filters.AddFilter(blockAttributeKey, fmt.Sprintf("%d", end), object.MatchNumLT)
+					if end == start+1 {
+						filters.AddFilter(blockAttributeKey, fmt.Sprintf("%d", start), object.MatchStringEqual)
+					} else {
+						filters.AddFilter(blockAttributeKey, fmt.Sprintf("%d", start), object.MatchNumGE)
+						filters.AddFilter(blockAttributeKey, fmt.Sprintf("%d", end), object.MatchNumLT)
+					}
 					prm.SetFilters(filters)
 
 					var objIDs []oid.ID
diff --git a/docs/neofs-blockstorage.md b/docs/neofs-blockstorage.md
index 46dfd5502..b251090ef 100644
--- a/docs/neofs-blockstorage.md
+++ b/docs/neofs-blockstorage.md
@@ -47,8 +47,7 @@ parameter.
     Depending on the mode, the service either:
    - Searches for index files by index file attribute and reads block OIDs from index
      file object-by-object.
-   - Searches batches of blocks directly by block attribute (the batch size is
-     configured via `OIDBatchSize` parameter).
+   - Searches blocks one by one directly by block attribute.
 
    Once the OIDs are retrieved, they are immediately redirected to the 
    block downloading routines for further processing. The channel that 
diff --git a/pkg/services/blockfetcher/blockfetcher.go b/pkg/services/blockfetcher/blockfetcher.go
index 5889c72c3..3b815dcdb 100644
--- a/pkg/services/blockfetcher/blockfetcher.go
+++ b/pkg/services/blockfetcher/blockfetcher.go
@@ -342,7 +342,8 @@ func (bfs *Service) streamBlockOIDs(rc io.ReadCloser, skip int) error {
 // fetchOIDsBySearch fetches block OIDs from NeoFS by searching through the Block objects.
 func (bfs *Service) fetchOIDsBySearch() error {
 	startIndex := bfs.chain.BlockHeight()
-	batchSize := uint32(bfs.cfg.OIDBatchSize)
+	//We need to search with EQ filter to avoid partially-completed SEARCH responses.
+	batchSize := uint32(1)
 
 	for {
 		select {
@@ -351,8 +352,12 @@ func (bfs *Service) fetchOIDsBySearch() error {
 		default:
 			prm := client.PrmObjectSearch{}
 			filters := object.NewSearchFilters()
-			filters.AddFilter(bfs.cfg.BlockAttribute, fmt.Sprintf("%d", startIndex), object.MatchNumGE)
-			filters.AddFilter(bfs.cfg.BlockAttribute, fmt.Sprintf("%d", startIndex+batchSize-1), object.MatchNumLE)
+			if startIndex == startIndex+batchSize-1 {
+				filters.AddFilter(bfs.cfg.BlockAttribute, fmt.Sprintf("%d", startIndex), object.MatchStringEqual)
+			} else {
+				filters.AddFilter(bfs.cfg.BlockAttribute, fmt.Sprintf("%d", startIndex), object.MatchNumGE)
+				filters.AddFilter(bfs.cfg.BlockAttribute, fmt.Sprintf("%d", startIndex+batchSize-1), object.MatchNumLE)
+			}
 			prm.SetFilters(filters)
 			ctx, cancel := context.WithTimeout(bfs.ctx, bfs.cfg.Timeout)
 			blockOids, err := bfs.objectSearch(ctx, prm)