diff --git a/mne/_fiff/tag.py b/mne/_fiff/tag.py
index 6a4636ef264..7f53cd21bf5 100644
--- a/mne/_fiff/tag.py
+++ b/mne/_fiff/tag.py
@@ -361,9 +361,9 @@ def _read_old_pack(fid, tag, shape, rlims):
 
 def _read_dir_entry_struct(fid, tag, shape, rlims):
     """Read dir entry struct tag."""
-    pos = tag.pos + 16
+    pos = tag.pos
     entries = list()
-    for offset in range(1, tag.size // 16):
+    for offset in range(tag.size // 16):
         ent = _read_tag_header(fid, pos + offset * 16)
         # The position of the real tag on disk is stored in the "next" entry within the
         # directory, so we need to overwrite ent.pos. For safety let's also overwrite
diff --git a/mne/io/fiff/raw.py b/mne/io/fiff/raw.py
index f9e10a0039d..f6b2027d8f5 100644
--- a/mne/io/fiff/raw.py
+++ b/mne/io/fiff/raw.py
@@ -231,7 +231,6 @@ def _read_raw_file(
             nchan = int(info["nchan"])
             first = 0
             first_samp = 0
-            first_skip = 0
 
             #   Get first sample tag if it is there
             if directory[first].kind == FIFF.FIFF_FIRST_SAMPLE:
@@ -240,14 +239,6 @@ def _read_raw_file(
                 first += 1
                 _check_entry(first, nent)
 
-            #   Omit initial skip
-            if directory[first].kind == FIFF.FIFF_DATA_SKIP:
-                # This first skip can be applied only after we know the bufsize
-                tag = read_tag(fid, directory[first].pos)
-                first_skip = int(tag.data.item())
-                first += 1
-                _check_entry(first, nent)
-
             raw = _RawShell()
             raw.first_samp = first_samp
             if info["meas_date"] is None and annotations is not None:
@@ -281,6 +272,9 @@ def _read_raw_file(
                 FIFF.FIFFT_COMPLEX_DOUBLE: "double",
             }
 
+            nskip = 0
+            nskip_in_samples = 0
+            first_data_buffer = True
             for k in range(first, nent):
                 ent = directory[k]
                 # There can be skips in the data (e.g., if the user unclicked)
@@ -297,24 +291,28 @@ def _read_raw_file(
                     if orig_format is None:
                         orig_format = _orig_format_dict[ent.type]
 
-                    #  Do we have an initial skip pending?
-                    if first_skip > 0:
-                        first_samp += nsamp * first_skip
-                        raw.first_samp = first_samp
-                        first_skip = 0
-
                     #  Do we have a skip pending?
                     if nskip > 0:
+                        nskip_in_samples += nskip * nsamp
+                        nskip = 0
+
+                    if nskip_in_samples > 0:
                         raw_extras.append(
                             dict(
                                 ent=None,
                                 first=first_samp,
-                                nsamp=nskip * nsamp,
-                                last=first_samp + nskip * nsamp - 1,
+                                nsamp=nskip_in_samples,
+                                last=first_samp + nskip_in_samples - 1,
                             )
                         )
-                        first_samp += nskip * nsamp
-                        nskip = 0
+                        first_samp += nskip_in_samples
+                        nskip_in_samples = 0
+
+                    #  Handle an initial skip.
+
+                    if first_data_buffer:
+                        raw.first_samp = first_samp
+                        first_data_buffer = False
 
                     #  Add a data buffer
                     raw_extras.append(
@@ -328,7 +326,10 @@ def _read_raw_file(
                     first_samp += nsamp
                 elif ent.kind == FIFF.FIFF_DATA_SKIP:
                     tag = read_tag(fid, ent.pos)
-                    nskip = int(tag.data.item())
+                    nskip += int(tag.data.item())
+                elif ent.kind == FIFF.FIFF_DATA_SKIP_SAMP:
+                    tag = read_tag(fid, ent.pos)
+                    nskip_in_samples += int(tag.data.item())
 
             next_fname = _get_next_fname(fid, _path_from_fname(fname), tree)