diff --git a/swh/core/db/db_utils.py b/swh/core/db/db_utils.py
--- a/swh/core/db/db_utils.py
+++ b/swh/core/db/db_utils.py
@@ -3,6 +3,7 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
+from contextlib import contextmanager
 from datetime import datetime, timezone
 import functools
 from importlib import import_module
@@ -11,7 +12,7 @@
 import pathlib
 import re
 import subprocess
-from typing import Collection, Dict, List, Optional, Tuple, Union, cast
+from typing import Collection, Dict, Iterator, List, Optional, Tuple, Union, cast
 
 import psycopg2
 import psycopg2.errors
@@ -58,28 +59,32 @@
     return value
 
 
-def connect_to_conninfo(db_or_conninfo: Union[str, pgconnection]) -> pgconnection:
-    """Connect to the database passed in argument
+@contextmanager
+def connect_to_conninfo(
+    db_or_conninfo: Union[str, pgconnection]
+) -> Iterator[pgconnection]:
+    """Connect to the database passed as argument.
 
     Args:
         db_or_conninfo: A database connection, or a database connection info string
 
     Returns:
-        a connected database handle
+        a connected database handle or None if the database is not initialized
 
-    Raises:
-        psycopg2.Error if the database doesn't exist
     """
     if isinstance(db_or_conninfo, pgconnection):
-        return db_or_conninfo
-
-    if "=" not in db_or_conninfo and "//" not in db_or_conninfo:
-        # Database name
-        db_or_conninfo = f"dbname={db_or_conninfo}"
-
-    db = psycopg2.connect(db_or_conninfo)
+        yield db_or_conninfo
+    else:
+        if "=" not in db_or_conninfo and "//" not in db_or_conninfo:
+            # Database name
+            db_or_conninfo = f"dbname={db_or_conninfo}"
 
-    return db
+    try:
+        db = psycopg2.connect(db_or_conninfo)
+    except psycopg2.Error:
+        logger.exception("Failed to connect to `%s`", db_or_conninfo)
+    else:
+        yield db
 
 
 def swh_db_version(db_or_conninfo: Union[str, pgconnection]) -> Optional[int]:
@@ -94,22 +99,18 @@
         Either the version of the database, or None if it couldn't be detected
     """
     try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
-
-    try:
-        with db.cursor() as c:
-            query = "select version from dbversion order by dbversion desc limit 1"
-            try:
-                c.execute(query)
-                result = c.fetchone()
-                if result:
-                    return result[0]
-            except psycopg2.errors.UndefinedTable:
+        with connect_to_conninfo(db_or_conninfo) as db:
+            if not db:
                 return None
+            with db.cursor() as c:
+                query = "select version from dbversion order by dbversion desc limit 1"
+                try:
+                    c.execute(query)
+                    result = c.fetchone()
+                    if result:
+                        return result[0]
+                except psycopg2.errors.UndefinedTable:
+                    return None
     except Exception:
         logger.exception("Could not get version from `%s`", db_or_conninfo)
     return None
@@ -129,23 +130,19 @@
         Either the version of the database, or None if it couldn't be detected
     """
     try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
-
-    try:
-        with db.cursor() as c:
-            query = (
-                "select version, release, description "
-                "from dbversion order by dbversion desc"
-            )
-            try:
-                c.execute(query)
-                return cast(List[Tuple[int, datetime, str]], c.fetchall())
-            except psycopg2.errors.UndefinedTable:
+        with connect_to_conninfo(db_or_conninfo) as db:
+            if not db:
                 return None
+            with db.cursor() as c:
+                query = (
+                    "select version, release, description "
+                    "from dbversion order by dbversion desc"
+                )
+                try:
+                    c.execute(query)
+                    return cast(List[Tuple[int, datetime, str]], c.fetchall())
+                except psycopg2.errors.UndefinedTable:
+                    return None
     except Exception:
         logger.exception("Could not get versions from `%s`", db_or_conninfo)
         return None
@@ -238,22 +235,18 @@
         Either the module of the database, or None if it couldn't be detected
     """
     try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
-
-    try:
-        with db.cursor() as c:
-            query = "select dbmodule from dbmodule limit 1"
-            try:
-                c.execute(query)
-                resp = c.fetchone()
-                if resp:
-                    return resp[0]
-            except psycopg2.errors.UndefinedTable:
+        with connect_to_conninfo(db_or_conninfo) as db:
+            if not db:
                 return None
+            with db.cursor() as c:
+                query = "select dbmodule from dbmodule limit 1"
+                try:
+                    c.execute(query)
+                    resp = c.fetchone()
+                    if resp:
+                        return resp[0]
+                except psycopg2.errors.UndefinedTable:
+                    return None
     except Exception:
         logger.exception("Could not get module from `%s`", db_or_conninfo)
     return None
@@ -289,27 +282,25 @@
             )
         # force is True
         update = True
-    try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
 
-    sqlfiles = [
-        fname
-        for fname in get_sql_for_package("swh.core.db")
-        if "dbmodule" in fname.stem
-    ]
-    execute_sqlfiles(sqlfiles, db_or_conninfo)
+    with connect_to_conninfo(db_or_conninfo) as db:
+        if not db:
+            return None
 
-    with db.cursor() as c:
-        if update:
-            query = "update dbmodule set dbmodule = %s"
-        else:
-            query = "insert into dbmodule(dbmodule) values (%s)"
-        c.execute(query, (module,))
-    db.commit()
+        sqlfiles = [
+            fname
+            for fname in get_sql_for_package("swh.core.db")
+            if "dbmodule" in fname.stem
+        ]
+        execute_sqlfiles(sqlfiles, db_or_conninfo)
+
+        with db.cursor() as c:
+            if update:
+                query = "update dbmodule set dbmodule = %s"
+            else:
+                query = "insert into dbmodule(dbmodule) values (%s)"
+            c.execute(query, (module,))
+        db.commit()
 
 
 def swh_set_db_version(
@@ -326,20 +317,19 @@
       db_or_conninfo: A database connection, or a database connection info string
       version: the version to add
     """
-    try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
     if ts is None:
         ts = now()
-    with db.cursor() as c:
-        query = (
-            "insert into dbversion(version, release, description) values (%s, %s, %s)"
-        )
-        c.execute(query, (version, ts, desc))
-    db.commit()
+
+    with connect_to_conninfo(db_or_conninfo) as db:
+        if not db:
+            return None
+        with db.cursor() as c:
+            query = (
+                "insert into dbversion(version, release, description) "
+                "values (%s, %s, %s)"
+            )
+            c.execute(query, (version, ts, desc))
+            db.commit()
 
 
 def swh_db_flavor(db_or_conninfo: Union[str, pgconnection]) -> Optional[str]:
@@ -355,23 +345,19 @@
         The flavor of the database, or None if it could not be detected.
     """
     try:
-        db = connect_to_conninfo(db_or_conninfo)
-    except psycopg2.Error:
-        logger.exception("Failed to connect to `%s`", db_or_conninfo)
-        # Database not initialized
-        return None
-
-    try:
-        with db.cursor() as c:
-            query = "select swh_get_dbflavor()"
-            try:
-                c.execute(query)
-                result = c.fetchone()
-                assert result is not None  # to keep mypy happy
-                return result[0]
-            except psycopg2.errors.UndefinedFunction:
-                # function not found: no flavor
+        with connect_to_conninfo(db_or_conninfo) as db:
+            if not db:
                 return None
+            with db.cursor() as c:
+                query = "select swh_get_dbflavor()"
+                try:
+                    c.execute(query)
+                    result = c.fetchone()
+                    assert result is not None  # to keep mypy happy
+                    return result[0]
+                except psycopg2.errors.UndefinedFunction:
+                    # function not found: no flavor
+                    return None
     except Exception:
         logger.exception("Could not get flavor from `%s`", db_or_conninfo)
         return None