diff --git a/concrete/numpy/__init__.py b/concrete/numpy/__init__.py
index 0a3d3355a..1ad2e263a 100644
--- a/concrete/numpy/__init__.py
+++ b/concrete/numpy/__init__.py
@@ -5,6 +5,8 @@ Export everything that users might need.
 from concrete.compiler import EvaluationKeys, PublicArguments, PublicResult
 
 from .compilation import (
+    DEFAULT_GLOBAL_P_ERROR,
+    DEFAULT_P_ERROR,
     Circuit,
     Client,
     ClientSpecs,
diff --git a/concrete/numpy/compilation/__init__.py b/concrete/numpy/compilation/__init__.py
index 05b4f1770..7fa7edf3a 100644
--- a/concrete/numpy/compilation/__init__.py
+++ b/concrete/numpy/compilation/__init__.py
@@ -6,6 +6,6 @@ from .artifacts import DebugArtifacts
 from .circuit import Circuit
 from .client import Client
 from .compiler import Compiler, EncryptionStatus
-from .configuration import Configuration
+from .configuration import DEFAULT_GLOBAL_P_ERROR, DEFAULT_P_ERROR, Configuration
 from .server import Server
 from .specs import ClientSpecs
diff --git a/concrete/numpy/compilation/configuration.py b/concrete/numpy/compilation/configuration.py
index 98763b5a4..6b9fa4182 100644
--- a/concrete/numpy/compilation/configuration.py
+++ b/concrete/numpy/compilation/configuration.py
@@ -6,6 +6,9 @@ from copy import deepcopy
 from pathlib import Path
 from typing import Optional, Union, get_type_hints
 
+DEFAULT_P_ERROR = None
+DEFAULT_GLOBAL_P_ERROR = 1 / 100_000
+
 
 class Configuration:
     """
@@ -70,7 +73,7 @@ class Configuration:
         auto_parallelize: bool = False,
         jit: bool = False,
         p_error: Optional[float] = None,
-        global_p_error: Optional[float] = (1 / 100_000),
+        global_p_error: Optional[float] = None,
         auto_adjust_rounders: bool = False,
     ):
         self.verbose = verbose
diff --git a/concrete/numpy/compilation/server.py b/concrete/numpy/compilation/server.py
index f7c78e88b..e9313d1c8 100644
--- a/concrete/numpy/compilation/server.py
+++ b/concrete/numpy/compilation/server.py
@@ -23,7 +23,7 @@ from concrete.compiler import (
 )
 
 from ..internal.utils import assert_that
-from .configuration import Configuration
+from .configuration import DEFAULT_GLOBAL_P_ERROR, DEFAULT_P_ERROR, Configuration
 from .specs import ClientSpecs
 
 
@@ -110,6 +110,17 @@ class Server:
             options.set_global_p_error(1.0)
             options.set_p_error(configuration.p_error)
 
+        else:  # pragma: no cover
+            if DEFAULT_GLOBAL_P_ERROR is not None:
+                options.set_global_p_error(DEFAULT_GLOBAL_P_ERROR)
+            else:
+                options.set_global_p_error(1.0)
+
+            if DEFAULT_P_ERROR is not None:
+                options.set_p_error(DEFAULT_P_ERROR)
+            else:
+                options.set_p_error(1.0)
+
         show_optimizer = (
             configuration.show_optimizer
             if configuration.show_optimizer is not None
diff --git a/docs/getting-started/exactness.md b/docs/getting-started/exactness.md
index d1ef5d881..18d6afe9e 100644
--- a/docs/getting-started/exactness.md
+++ b/docs/getting-started/exactness.md
@@ -18,7 +18,7 @@ However, if you set `global_p_error` to `0.01`, the whole circuit will have 1% p
 
 If you set both of them, both will be satisfied. Essentially, the stricter one will be used.
 
-By default, `p_error` is set to `None` and `global_p_error` is set to `1 / 100_000`. Feel free to play with these configuration options to pick the one best suited for your needs! For example, in some machine learning use cases, off-by-one or off-by-two errors doesn't affect the result much, in such cases `p_error` could be set to increase performance without losing accuracy.
+By default, both `p_error` and `global_p_error` is set to `None`, which results in `global_p_error` of `1 / 100_000` being used. Feel free to play with these configuration options to pick the one best suited for your needs! For example, in some machine learning use cases, off-by-one or off-by-two errors doesn't affect the result much, in such cases `p_error` could be set to increase performance without losing accuracy.
 
 See [How to Configure](../howto/configure.md) to learn how you can set a custom `p_error` and/or `global_p_error`.
 
diff --git a/docs/howto/configure.md b/docs/howto/configure.md
index 3e8ddc69d..2f3216f5f 100644
--- a/docs/howto/configure.md
+++ b/docs/howto/configure.md
@@ -74,10 +74,10 @@ Additional kwarg to `compile` function have higher precedence. So if you set an
     * Whether to adjust rounders automatically.
 
 * **p_error**: Optional[float] = None
-  * Error probability for individual table lookups. If set, all table lookups will have the probability of non-exact result smaller than the set value.
+  * Error probability for individual table lookups. If set, all table lookups will have the probability of non-exact result smaller than the set value. See [Exactness](../getting-started/exactness.md) to learn more.
 
-* **global_p_error**: Optional[float] = (1 / 100_000)
-    * Global error probability for the whole circuit. If set, the whole circuit will have the probability of non-exact result smaller than the set value.
+* **global_p_error**: Optional[float] = None
+    * Global error probability for the whole circuit. If set, the whole circuit will have the probability of non-exact result smaller than the set value. See [Exactness](../getting-started/exactness.md) to learn more.
 
 * **jit**: bool = False
   * Whether to use JIT compilation.