diff --git a/CHANGELOG.md b/CHANGELOG.md
index e4ce3fb..a4a0518 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,15 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.1.0/).
 This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html) for its CLI (Command-Line Interface), i.e. for the `moulti` command.
 Although Moulti's Python packages, modules and functions are obviously available, they do not constitute a public API yet.
 
+## Unreleased
+
+### Changed
+
+- `moulti run` now suffixes the instance name with its process id (e.g. `default-1234` instead of `default`).
+  This helps prevent clashes and makes it possible to run various tools concurrently without having to worry about such details.
+  This behaviour can be prevented by setting the `MOULTI_RUN_NO_SUFFIX` environment variable or using the `-n` / `--no-suffix` command-line option.
+  The behaviour of `moulti init` remains unchanged.
+
 ## [1.29.0] - 2025-01-12
 
 ### Changed
diff --git a/Documentation.md b/Documentation.md
index be7113e..2d8201f 100644
--- a/Documentation.md
+++ b/Documentation.md
@@ -114,22 +114,23 @@ Limitation: shell completion will help typing subcommands and options but is tec
 ## Shell scripting
 
 The key takeaway from the previous section is that Moulti starts as an empty shell that is meant to be controlled and filled through the `moulti` CLI tool.
-A simple Moulti-based bash script makes use of two new commands:
+Controlling a Moulti instance by typing individual commands is occasionally useful but, most of the time, Moulti is driven by a shell script.
+To this end, a new subcommand proves helpful: `moulti run`.
+`moulti run` is essentially the same as `moulti init` but it runs a command right after the startup phase.
 
-- `moulti run`: same as `moulti init` but runs a command right after the startup phase
-- `moulti wait`: tries connecting to the Moulti instance; think "ping for moulti"
+That command inherits various environment variables; among them:
+- `MOULTI_RUN`: if this variable is set to a non-empty value, the Moulti instance is already running and there is no need to launch it;
+- `MOULTI_SOCKET_PATH`: this variable ensures all subsequent `moulti` commands connect to the right Moulti instance.
 
-... and looks like this:
+In practice, a simple Moulti-based bash script looks like this:
 
 ```bash
 #!/usr/bin/env bash
 
-# Name the Moulti instance to prevent conflicts:
+# Good practice: name the Moulti instance:
 export MOULTI_INSTANCE='my-first-script-with-moulti'
 # If not done already, start a Moulti instance and have it re-execute this script:
 [ "${MOULTI_RUN}" ] || exec moulti run -- "$0" "$@"
-# Ensure the Moulti instance is reachable:
-moulti wait
 moulti step add step_1 --title='First step'
 {
    echo "$(date --iso-8601=ns) Starting combobulating things and stuff..."
@@ -142,7 +143,7 @@ moulti step add step_2 --title='Second step'
 } 2>&1 | moulti pass step_2
 ```
 
-In practice, it makes sense to heavily leverage shell functions, such as those available in [moulti-functions.bash](examples/moulti-functions.bash).
+In real life, it makes sense to heavily leverage shell functions, such as those available in [moulti-functions.bash](examples/moulti-functions.bash).
 
 ### Dealing with existing scripts
 
@@ -930,7 +931,8 @@ Hit `n` to go to the next occurrence or `N` to go to the previous one.
 
 #### Connectivity
 
-- `MOULTI_INSTANCE`: name of your Moulti instance; defaults to `default`; taken into account by the instance to compute the default value of `MOULTI_SOCKET_PATH`.
+- `MOULTI_INSTANCE`: name of your Moulti instance; defaults to `default`; `moulti init` keeps this value untouched; since v1.30.0, `moulti run` appends its process id (e.g. `default-1234`) to prevent conflicts; taken into account by the instance to compute the default value of `MOULTI_SOCKET_PATH`.
+- `MOULTI_RUN_NO_SUFFIX`: if non-empty, instruct `moulti run` not to append its process id to the instance name; setting this environment variable is equivalent to running `moulti run --no-suffix`.
 - `MOULTI_SOCKET_PATH`: path to the network socket that Moulti should listen/connect to; taken into account by both the instance and the CLI; if not specified, Moulti defaults to a platform-specific value that reflects your username and `MOULTI_INSTANCE`; examples: `@moulti-bob-test-instance.socket`, `/run/user/1000/moulti-bob-test-instance.socket`.
 - `MOULTI_ALLOWED_UID`: abstract sockets (i.e. Linux) only! By default, Moulti only accepts commands from the user (uid) that launched the Moulti instance; setting this environment variable beforehand makes it accept arbitrary uids; example:
   ```shell
diff --git a/examples/moulti-man b/examples/moulti-man
index 3c0be45..c50a900 100755
--- a/examples/moulti-man
+++ b/examples/moulti-man
@@ -15,4 +15,4 @@ max_unindent=3
 export MANWIDTH=$(((COLUMNS-moulti_columns+max_unindent)))
 
 export MOULTI_INSTANCE="man-$$"
-exec moulti run -- moulti manpage run -- man "$@"
+exec moulti run --no-suffix -- moulti manpage run -- man "$@"
diff --git a/examples/moulti-scoreboard.bash b/examples/moulti-scoreboard.bash
index b4c631f..910d710 100755
--- a/examples/moulti-scoreboard.bash
+++ b/examples/moulti-scoreboard.bash
@@ -73,7 +73,7 @@ if [ -z "${MOULTI_RUN}" ]; then
 	[ "${SCOREBOARD_COLUMNS}" ] && export COLUMNS="${SCOREBOARD_COLUMNS}"
 	[ "${SCOREBOARD_LINES}" ] && export LINES="${SCOREBOARD_LINES}"
 
-	exec moulti run -- "$0" "$@"
+	exec moulti run --no-suffix -- "$0" "$@"
 fi
 
 # Part 3: driver script:
diff --git a/src/moulti/cli.py b/src/moulti/cli.py
index 069edd4..509b261 100644
--- a/src/moulti/cli.py
+++ b/src/moulti/cli.py
@@ -7,8 +7,8 @@
 from typing import Generator
 import argcomplete
 from . import __version__ as moulti_version
-from .client import moulti_socket_path, send_to_moulti, send_to_moulti_and_handle_reply, pipeline
-from .environ import pint, float_str
+from .client import current_instance, moulti_socket_path, send_to_moulti, send_to_moulti_and_handle_reply, pipeline
+from .environ import env, pint, float_str
 from .widgets.cli import add_cli_arguments
 from .manpage import manpage_parse, manpage_run
 
@@ -18,8 +18,26 @@ def init(args: dict) -> None:
 	from .app import main as init_moulti # pylint: disable=import-outside-toplevel
 	init_moulti(**args)
 
+def moulti_run_should_suffix_instance_name(args: dict) -> bool:
+	"""
+	By default, `moulti run` suffixes the instance name with the process id.
+	Since the socket path is derived from the instance name, this helps prevent clashes and thus
+	"cannot listen" errors.
+	"""
+	if env('MOULTI_SOCKET_PATH'):
+		# If a socket path was explicitly set, then the instance name cannot affect
+		# its computation. Therefore, there is no need to suffix the instance name.
+		return False
+	if args['no_suffix']:
+		return False
+	if env('MOULTI_RUN_NO_SUFFIX') is not None:
+		return False
+	return True
+
 def run(args: dict) -> None:
 	"""Start a new Moulti instance and run the given command."""
+	if moulti_run_should_suffix_instance_name(args):
+		os.environ['MOULTI_INSTANCE'] = f'{current_instance()}-{os.getpid()}'
 
 	# Handle --print-env:
 	if args['print_env']:
@@ -96,6 +114,7 @@ def add_main_commands(subparsers: _SubParsersAction) -> None:
 	run_parser = subparsers.add_parser('run', help='start a new Moulti instance and run a command')
 	run_parser.set_defaults(func=run)
 	run_parser.add_argument('--print-env', action='store_true', default=False, help='print environment variables set by Moulti and exit')
+	run_parser.add_argument('--no-suffix', '-n', action='store_true', default=False, help='do not suffix the instance name with the process id')
 	run_parser.add_argument('command', type=str, nargs='+', help='command to run along with its arguments')
 
 	# moulti wait