diff --git a/conans/client/graph/graph_binaries.py b/conans/client/graph/graph_binaries.py
index d8a81deeddb..d759f8d6d38 100644
--- a/conans/client/graph/graph_binaries.py
+++ b/conans/client/graph/graph_binaries.py
@@ -100,9 +100,11 @@ def _evaluate_cache_pkg(self, node, package_layout, pref, metadata, remote, remo
     def _get_package_info(self, node, pref, remote):
         return self._remote_manager.get_package_info(pref, remote, info=node.conanfile.info)
 
-    def _evaluate_remote_pkg(self, node, pref, remote, remotes):
+    def _evaluate_remote_pkg(self, node, pref, remote, remotes, remote_selected):
         remote_info = None
-        if remote:
+        # If the remote is pinned (remote_selected) we won't iterate the remotes.
+        # The "remote" can come from -r or from the registry (associated ref)
+        if remote_selected or remote:
             try:
                 remote_info, pref = self._get_package_info(node, pref, remote)
             except NotFoundException:
@@ -111,10 +113,16 @@ def _evaluate_remote_pkg(self, node, pref, remote, remotes):
                 node.conanfile.output.error("Error downloading binary package: '{}'".format(pref))
                 raise
 
-        # If the "remote" came from the registry but the user didn't specified the -r, with
-        # revisions iterate all remotes
-        if not remote or (not remote_info and self._cache.config.revisions_enabled):
-            for r in remotes.values():  # FIXME: Here we hit the same remote we did before
+        # If we didn't pin a remote with -r and:
+        #   - The remote is None (not registry entry)
+        #        or
+        #   - We didn't find a package but having revisions enabled
+        # We iterate the other remotes to find a binary
+        if not remote_selected and (not remote or
+                                    (not remote_info and self._cache.config.revisions_enabled)):
+            for r in remotes.values():
+                if r == remote:
+                    continue
                 try:
                     remote_info, pref = self._get_package_info(node, pref, r)
                 except NotFoundException:
@@ -243,6 +251,7 @@ def _process_node(self, node, pref, build_mode, update, remotes):
         metadata = self._evaluate_clean_pkg_folder_dirty(node, package_layout, pref)
 
         remote = remotes.selected
+        remote_selected = remote is not None
 
         metadata = metadata or package_layout.load_metadata()
         if not remote:
@@ -260,7 +269,8 @@ def _process_node(self, node, pref, build_mode, update, remotes):
             recipe_hash = None
         else:  # Binary does NOT exist locally
             # Returned remote might be different than the passed one if iterating remotes
-            recipe_hash, remote = self._evaluate_remote_pkg(node, pref, remote, remotes)
+            recipe_hash, remote = self._evaluate_remote_pkg(node, pref, remote, remotes,
+                                                            remote_selected)
 
         if build_mode.outdated:
             if node.binary in (BINARY_CACHE, BINARY_DOWNLOAD, BINARY_UPDATE):
diff --git a/conans/test/functional/revisions_test.py b/conans/test/functional/revisions_test.py
index 94c9f25473d..b4f31113fe1 100644
--- a/conans/test/functional/revisions_test.py
+++ b/conans/test/functional/revisions_test.py
@@ -1598,3 +1598,20 @@ def test_necessary_update():
     c.save({"conanfile.py": GenConanfile("app", "0.1").with_requires("pkg/0.1#{}".format(rrev2))})
     c.run("install .")
     assert rrev2 in c.out
+
+
+def test_touching_other_server():
+    # https://github.com/conan-io/conan/issues/9333
+    servers = OrderedDict([("remote1", TestServer()),
+                           ("remote2", None)])  # None server will crash if touched
+    c = TestClient(servers=servers, users={"remote1": [("conan", "password")]})
+    c.run("config set general.revisions_enabled=True")
+    c.save({"conanfile.py": GenConanfile().with_settings("os")})
+    c.run("create . pkg/0.1@conan/channel -s os=Windows")
+    c.run("upload * --all -c -r=remote1")
+    c.run("remove * -f")
+
+    # This is OK, binary found
+    c.run("install pkg/0.1@conan/channel -r=remote1 -s os=Windows")
+    c.run("install pkg/0.1@conan/channel -r=remote1 -s os=Linux", assert_error=True)
+    assert "ERROR: Missing binary: pkg/0.1@conan/channel" in c.out
diff --git a/conans/test/integration/command/install/install_update_test.py b/conans/test/integration/command/install/install_update_test.py
index f802336f07f..39b4a0c96d9 100644
--- a/conans/test/integration/command/install/install_update_test.py
+++ b/conans/test/integration/command/install/install_update_test.py
@@ -290,6 +290,7 @@ def test_fail_usefully_when_failing_retrieving_package():
     client.run("install {}".format(ref2), assert_error=True)
     assert "ERROR: Error downloading binary package: '{}'".format(pref1) in client.out
 
+
 def test_evil_insertions():
     ref = ConanFileReference.loads("lib1/1.0@conan/stable")
     ref2 = ConanFileReference.loads("lib2/1.0@conan/stable")
diff --git a/conans/test/integration/remote/test_request_headers.py b/conans/test/integration/remote/test_request_headers.py
index 29c61cb828c..4cea918ab66 100644
--- a/conans/test/integration/remote/test_request_headers.py
+++ b/conans/test/integration/remote/test_request_headers.py
@@ -50,7 +50,7 @@ def setUp(self):
 
     def _get_header(self, requester, header_name):
         hits = sum([header_name in headers for _, headers in requester.requests])
-        assert hits == 2 if self.revs_enabled else 1
+        assert hits <= 2 if self.revs_enabled else 1
         for url, headers in requester.requests:
             if header_name in headers:
                 if self.revs_enabled: