diff --git a/doc/theoretical_description_multilabel_classification.rst b/doc/theoretical_description_multilabel_classification.rst
index f8502eb5e..f8aff6a2d 100644
--- a/doc/theoretical_description_multilabel_classification.rst
+++ b/doc/theoretical_description_multilabel_classification.rst
@@ -16,7 +16,7 @@ our training data :math:`(X, Y) = \{(x_1, y_1), \ldots, (x_n, y_n)\}`` has an un
 
 For any risk level :math:`\alpha` between 0 and 1, the methods implemented in MAPIE allow the user to construct a prediction
 set :math:`\hat{C}_{n, \alpha}(X_{n+1})` for a new observation :math:`\left( X_{n+1},Y_{n+1} \right)` with a guarantee
-on the recall or the precision. RCPS, LTT and CRC give three slightly different guarantees:
+on the recall. RCPS, LTT and CRC give three slightly different guarantees:
 
 - RCPS:
 
@@ -32,6 +32,8 @@ on the recall or the precision. RCPS, LTT and CRC give three slightly different
 .. math::
     \mathbb{P}(R(\mathcal{T}_{\lambda_{\lambda\in\hat{\Lambda}}) \leq \alpha ) \geq 1 - \delta
 
+Notice that at the opposite of the other two methods, LTT allows to control any non-monotone loss. In Mapie for multilabel classification,
+we use CRC and RCPS for recall control and LTT for precision control.
 
 1. Risk-Controlling Prediction Sets
 -----------------------------------
@@ -163,21 +165,22 @@ With :
 
 3. Learn Then Test
 ------------------
-The goal of this method is to control any loss whether monotone, bounded or not. The main goal of this method is to achieve risk control
-throught multiple hypothesis testing. We can express the goal of the procedure as follows:
+The goal of this method is to control any loss whether monotonic, bounded or not, by performing risk control through multiple
+hypothesis testing. We can express the goal of the procedure as follows:
 
 .. math::
     \mathbb{P}(R(\mathcal{T}_{\lambda}) \leq \alpha ) \geq 1 - \delta
 
 In order to find all the parameters :math:`\lambda` that satisfy the above condition, Learn Then Test propose to do the following:
 
-0: First across the collections of functions :math:`(T_\lambda)_{\lambda\in\Lambda}`, we estimate the risk on the calibration data
+1: First across the collections of functions :math:`(T_\lambda)_{\lambda\in\Lambda}`, we estimate the risk on the calibration data
 \{(x_1, y_1), \dots, (x_n, y_n)\}`.
-1: For each :math:`\lambda_j` in a discrete set :math:`\Lambda = \{\lambda_1, \lambda_2,\dots, \lambda_n\}`, we associate the null hypothesis
+2: For each :math:`\lambda_j` in a discrete set :math:`\Lambda = \{\lambda_1, \lambda_2,\dots, \lambda_n\}`, we associate the null hypothesis
 :math:`\mathbb{H}_j: R(\lambda_j)>\alpha`, as rejecting the hypothesis corresponds to selecting :math:`\lambda_j` as a point where risk the risk 
 is controlled.
-2: For each null hypothesis, we compute a valid p-value using a concentration inequality.
-3: Return :math:`\hat{\Lambda} =  \mathbb{A}(\{p_j\}_{j\in\{1,\dots,lvert \Lambda \rvert})`, where :math:`\mathbb{A}`, is an algorithm
+3: For each null hypothesis, we compute a valid p-value using a concentration inequality. Here we choose to compute the Hoeffding-Bentkus p-value
+introduced in the paper [3].
+4: Return :math:`\hat{\Lambda} =  \mathbb{A}(\{p_j\}_{j\in\{1,\dots,lvert \Lambda \rvert})`, where :math:`\mathbb{A}`, is an algorithm
 that controls the family-wise-error-rate (FWER).
 
 
diff --git a/mapie/control_risk/risks.py b/mapie/control_risk/risks.py
index 818576ca5..f396c7d2a 100644
--- a/mapie/control_risk/risks.py
+++ b/mapie/control_risk/risks.py
@@ -70,7 +70,7 @@ def _compute_risk_precision(
     y: NDArray
 ) -> NDArray:
     """
-    In `MapieMultiLabelClassifier` when`metric_control=precision`,
+    In `MapieMultiLabelClassifier` when `metric_control=precision`,
     compute the precision per observation for each different
     thresholds lambdas.