diff --git a/src/import/import-raw.c b/src/import/import-raw.c
index 9c2c74527f..fcb07751d2 100644
--- a/src/import/import-raw.c
+++ b/src/import/import-raw.c
@@ -368,7 +368,7 @@ static int raw_import_write(const void *p, size_t sz, void *userdata) {
         }
 
         /* Generate sparse file if we created/truncated the file */
-        if (S_ISREG(i->output_stat.st_mode)) {
+        if (S_ISREG(i->output_stat.st_mode) && i->offset == UINT64_MAX) {
                 ssize_t n;
 
                 n = sparse_write(i->output_fd, p, sz, 64);
diff --git a/src/import/pull-job.c b/src/import/pull-job.c
index fb869e7095..4e37dce33f 100644
--- a/src/import/pull-job.c
+++ b/src/import/pull-job.c
@@ -306,7 +306,7 @@ static int pull_job_write_uncompressed(const void *p, size_t sz, void *userdata)
 
         if (j->disk_fd >= 0) {
 
-                if (S_ISREG(j->disk_stat.st_mode)) {
+                if (S_ISREG(j->disk_stat.st_mode) && j->offset == UINT64_MAX) {
                         ssize_t n;
 
                         n = sparse_write(j->disk_fd, p, sz, 64);