diff --git a/swh/web/common/origin_visits.py b/swh/web/common/origin_visits.py
--- a/swh/web/common/origin_visits.py
+++ b/swh/web/common/origin_visits.py
@@ -8,6 +8,7 @@
 
 from django.core.cache import cache
 
+from swh.web.common import service
 from swh.web.common.exc import NotFoundExc
 from swh.web.common.typing import OriginInfo, OriginVisitInfo
 from swh.web.common.utils import parse_iso8601_date_to_utc
@@ -110,19 +111,17 @@
     Raises:
         swh.web.common.exc.NotFoundExc: if no visit can be found
     """
-
-    if not visit_ts and not visit_id and not snapshot_id:
-        from swh.web.common import service
-
-        # returns the latest full visit with a valid snapshot
+    # returns the latest full visit with a valid snapshot
+    visit = service.lookup_origin_visit_latest(
+        origin_info["url"], allowed_statuses=["full"], require_snapshot=True
+    )
+    if not visit:
+        # or the latest partial visit with a valid snapshot otherwise
         visit = service.lookup_origin_visit_latest(
-            origin_info["url"], allowed_statuses=["full"], require_snapshot=True
+            origin_info["url"], allowed_statuses=["partial"], require_snapshot=True
         )
-        if not visit:
-            # or the latest partial visit with a valid snapshot otherwise
-            visit = service.lookup_origin_visit_latest(
-                origin_info["url"], allowed_statuses=["partial"], require_snapshot=True
-            )
+
+    if not visit_ts and not visit_id and not snapshot_id:
         if visit:
             return visit
         else:
@@ -130,6 +129,11 @@
                 f"No valid visit for origin with url {origin_info['url']} found!"
             )
 
+    # no need to fetch all visits list and search in it if the latest
+    # visit matches some criteria
+    if visit and (visit["snapshot"] == snapshot_id or visit["visit"] == visit_id):
+        return visit
+
     visits = get_origin_visits(origin_info)
 
     if not visits:
diff --git a/swh/web/common/service.py b/swh/web/common/service.py
--- a/swh/web/common/service.py
+++ b/swh/web/common/service.py
@@ -21,7 +21,6 @@
 from swh.web.common import converters
 from swh.web.common import query
 from swh.web.common.exc import BadInputExc, NotFoundExc
-from swh.web.common.origin_visits import get_origin_visit
 from swh.web.common.typing import (
     OriginInfo,
     OriginVisitInfo,
@@ -568,6 +567,8 @@
     else:
         raise TypeError('"origin" must be an int or a string.')
 
+    from swh.web.common.origin_visits import get_origin_visit
+
     visit = get_origin_visit(origin, visit_ts=timestamp)
     branch = _get_snapshot_branch(visit["snapshot"], branch_name)
     rev_id = None
diff --git a/swh/web/tests/browse/views/test_origin.py b/swh/web/tests/browse/views/test_origin.py
--- a/swh/web/tests/browse/views/test_origin.py
+++ b/swh/web/tests/browse/views/test_origin.py
@@ -513,12 +513,14 @@
         "swh.web.common.origin_visits.get_origin_visits"
     )
     mock_get_origin_visits.return_value = []
+    mock_service = mocker.patch("swh.web.common.origin_visits.service")
+    mock_service.lookup_origin_visit_latest.return_value = None
     url = reverse("browse-origin-directory", query_params={"origin_url": origin["url"]})
     resp = client.get(url)
     assert resp.status_code == 404
     assert_template_used(resp, "error.html")
-    assert_contains(resp, "No visit", status_code=404)
-    assert mock_get_origin_visits.called
+    assert_contains(resp, "No valid visit", status_code=404)
+    assert not mock_get_origin_visits.called
 
 
 @given(origin())
@@ -557,6 +559,8 @@
         "swh.web.common.origin_visits.get_origin_visits"
     )
     mock_get_origin_visits.return_value = []
+    mock_service = mocker.patch("swh.web.common.origin_visits.service")
+    mock_service.lookup_origin_visit_latest.return_value = None
     url = reverse(
         "browse-origin-content",
         query_params={"origin_url": origin["url"], "path": "foo"},
@@ -564,8 +568,8 @@
     resp = client.get(url)
     assert resp.status_code == 404
     assert_template_used(resp, "error.html")
-    assert_contains(resp, "No visit", status_code=404)
-    assert mock_get_origin_visits.called
+    assert_contains(resp, "No valid visit", status_code=404)
+    assert not mock_get_origin_visits.called
 
 
 @given(origin())
diff --git a/swh/web/tests/common/test_origin_visits.py b/swh/web/tests/common/test_origin_visits.py
--- a/swh/web/tests/common/test_origin_visits.py
+++ b/swh/web/tests/common/test_origin_visits.py
@@ -15,7 +15,11 @@
 from swh.web.common.exc import NotFoundExc
 from swh.web.common.origin_visits import get_origin_visits, get_origin_visit
 from swh.web.common.typing import OriginInfo
-from swh.web.tests.strategies import new_origin, new_snapshots
+from swh.web.tests.strategies import (
+    new_origin,
+    new_snapshots,
+    origin_with_multiple_visits,
+)
 
 
 @given(new_snapshots(3))
@@ -233,3 +237,22 @@
     # should return the last visit
     expected_visit = archive_data.origin_visit_get_by(new_origin.url, visits[-1])
     assert get_origin_visit((OriginInfo(url=new_origin.url))) == expected_visit
+
+
+@given(origin_with_multiple_visits())
+def test_get_origin_visit_latest_snapshot(mocker, origin):
+    origin_visits = get_origin_visits(origin)
+    first_visit = origin_visits[0]
+    latest_visit = origin_visits[-1]
+    mock_get_origin_visits = mocker.patch(
+        "swh.web.common.origin_visits.get_origin_visits"
+    )
+    mock_get_origin_visits.return_value = origin_visits
+
+    visit = get_origin_visit(origin, snapshot_id=latest_visit["snapshot"])
+    assert visit == latest_visit
+    assert not mock_get_origin_visits.called
+
+    visit = get_origin_visit(origin, snapshot_id=first_visit["snapshot"])
+    assert visit == first_visit
+    assert mock_get_origin_visits.called