diff --git a/compose/cli/log_printer.py b/compose/cli/log_printer.py
index cd9f73c2c..c49b817de 100644
--- a/compose/cli/log_printer.py
+++ b/compose/cli/log_printer.py
@@ -16,18 +16,22 @@ from compose.utils import split_buffer
 
 class LogPresenter:
 
-    def __init__(self, prefix_width, color_func):
+    def __init__(self, prefix_width, color_func, keep_prefix=True):
         self.prefix_width = prefix_width
         self.color_func = color_func
+        self.keep_prefix = keep_prefix
 
     def present(self, container, line):
-        prefix = container.name_without_project.ljust(self.prefix_width)
-        return '{prefix} {line}'.format(
-            prefix=self.color_func(prefix + ' |'),
-            line=line)
+        to_log = '{line}'.format(line=line)
+
+        if self.keep_prefix:
+            prefix = container.name_without_project.ljust(self.prefix_width)
+            to_log = '{prefix} '.format(prefix=self.color_func(prefix + ' |')) + to_log
+
+        return to_log
 
 
-def build_log_presenters(service_names, monochrome):
+def build_log_presenters(service_names, monochrome, keep_prefix=True):
     """Return an iterable of functions.
 
     Each function can be used to format the logs output of a container.
@@ -38,7 +42,7 @@ def build_log_presenters(service_names, monochrome):
         return text
 
     for color_func in cycle([no_color] if monochrome else colors.rainbow()):
-        yield LogPresenter(prefix_width, color_func)
+        yield LogPresenter(prefix_width, color_func, keep_prefix)
 
 
 def max_name_width(service_names, max_index_width=3):
diff --git a/compose/cli/main.py b/compose/cli/main.py
index 626ef294a..6776dae9e 100644
--- a/compose/cli/main.py
+++ b/compose/cli/main.py
@@ -610,11 +610,12 @@ class TopLevelCommand:
         Usage: logs [options] [--] [SERVICE...]
 
         Options:
-            --no-color          Produce monochrome output.
-            -f, --follow        Follow log output.
-            -t, --timestamps    Show timestamps.
-            --tail="all"        Number of lines to show from the end of the logs
-                                for each container.
+            --no-color              Produce monochrome output.
+            -f, --follow            Follow log output.
+            -t, --timestamps        Show timestamps.
+            --tail="all"            Number of lines to show from the end of the logs
+                                    for each container.
+            --no-log-prefix    Don't print prefix in logs.
         """
         containers = self.project.containers(service_names=options['SERVICE'], stopped=True)
 
@@ -635,7 +636,8 @@ class TopLevelCommand:
             containers,
             set_no_color_if_clicolor(options['--no-color']),
             log_args,
-            event_stream=self.project.events(service_names=options['SERVICE'])).run()
+            event_stream=self.project.events(service_names=options['SERVICE']),
+            keep_prefix=not options['--no-log-prefix']).run()
 
     def pause(self, options):
         """
@@ -1017,6 +1019,7 @@ class TopLevelCommand:
                                        container. Implies --abort-on-container-exit.
             --scale SERVICE=NUM        Scale SERVICE to NUM instances. Overrides the
                                        `scale` setting in the Compose file if present.
+            --no-log-prefix       Don't print prefix in logs.
         """
         start_deps = not options['--no-deps']
         always_recreate_deps = options['--always-recreate-deps']
@@ -1028,6 +1031,7 @@ class TopLevelCommand:
         detached = options.get('--detach')
         no_start = options.get('--no-start')
         attach_dependencies = options.get('--attach-dependencies')
+        keep_prefix = not options['--no-log-prefix']
 
         if detached and (cascade_stop or exit_value_from or attach_dependencies):
             raise UserError(
@@ -1094,7 +1098,8 @@ class TopLevelCommand:
                 set_no_color_if_clicolor(options['--no-color']),
                 {'follow': True},
                 cascade_stop,
-                event_stream=self.project.events(service_names=service_names))
+                event_stream=self.project.events(service_names=service_names),
+                keep_prefix=keep_prefix)
             print("Attaching to", list_containers(log_printer.containers))
             cascade_starter = log_printer.run()
 
@@ -1382,10 +1387,11 @@ def log_printer_from_project(
     log_args,
     cascade_stop=False,
     event_stream=None,
+    keep_prefix=True,
 ):
     return LogPrinter(
         containers,
-        build_log_presenters(project.service_names, monochrome),
+        build_log_presenters(project.service_names, monochrome, keep_prefix),
         event_stream or project.events(),
         cascade_stop=cascade_stop,
         log_args=log_args)
diff --git a/tests/acceptance/cli_test.py b/tests/acceptance/cli_test.py
index d678130c1..a7ccd1489 100644
--- a/tests/acceptance/cli_test.py
+++ b/tests/acceptance/cli_test.py
@@ -3034,3 +3034,12 @@ services:
         another = self.project.get_service('--log-service')
         assert len(service.containers()) == 1
         assert len(another.containers()) == 1
+
+    def test_up_no_log_prefix(self):
+        self.base_dir = 'tests/fixtures/echo-services'
+        result = self.dispatch(['up', '--no-log-prefix'])
+
+        assert 'simple' in result.stdout
+        assert 'another' in result.stdout
+        assert 'exited with code 0' in result.stdout
+        assert 'exited with code 0' in result.stdout