diff --git a/R/dof.R b/R/dof.R
index 022a61501..fb777adde 100644
--- a/R/dof.R
+++ b/R/dof.R
@@ -3,39 +3,32 @@
 #' Estimate or extract degrees of freedom of models parameters.
 #'
 #' @param model A statistical model.
-#' @param method Can be `"analytical"` (default, DoFs are estimated based
-#'   on the model type), `"residual"` in which case they are directly taken
-#'   from the model if available (for Bayesian models, the goal (looking for
-#'   help to make it happen) would be to refit the model as a frequentist one
-#'   before extracting the DoFs), `"ml1"` (see [dof_ml1()]), `"betwithin"`
-#'   (see [dof_betwithin()]), `"satterthwaite"` (see [`dof_satterthwaite()`]),
-#'   `"kenward"` (see [`dof_kenward()`]) or `"any"`, which tries to extract DoF
-#'   by any of those methods, whichever succeeds. See 'Details'.
-#' @param ... Currently not used.
-#'
-#' @details
-#' Methods for calculating degrees of freedom:
+#' @param method Type of approximation for the degrees of freedom. Can be one of
+#' the following:
 #'
-#' - `"analytical"` for models of class `lmerMod`, Kenward-Roger approximated
-#'   degrees of freedoms are calculated, for other models, `n-k` (number of
-#'   observations minus number of parameters).
-#' - `"residual"` tries to extract residual degrees of freedom, and returns
-#'   `Inf` if residual degrees of freedom could not be extracted.
-#' - `"any"` first tries to extract residual degrees of freedom, and if these
-#'   are not available, extracts analytical degrees of freedom.
-#' - `"nokr"` same as `"analytical"`, but does not Kenward-Roger approximation
-#'   for models of class `lmerMod`. Instead, always uses `n-k` to calculate df
-#'   for any model.
-#' - `"normal"` returns `Inf`.
-#' - `"wald"` returns residual df for models with t-statistic, and `Inf` for all other models.
-#' - `"kenward"` calls [`dof_kenward()`].
-#' - `"satterthwaite"` calls [`dof_satterthwaite()`].
-#' - `"ml1"` calls [`dof_ml1()`].
-#' - `"betwithin"` calls [`dof_betwithin()`].
+#'   + `"residual"` (aka `"analytical"`) returns the residual degrees of
+#'     freedom, which usually is what [`stats::df.residual()`] returns. If a
+#'     model object has no method to extract residual degrees of freedom, these
+#'     are calculated as `n-p`, i.e. the number of observations minus the number
+#'     of estimated parameters. If residual degrees of freedom cannot be extracted
+#'     by either approach, returns `Inf`.
+#'   + `"wald"` returns residual (aka analytical) degrees of freedom for models
+#'     with t-statistic, `1` for models with Chi-squared statistic, and `Inf` for
+#'     all other models. Also returns `Inf` if residual degrees of freedom cannot
+#'     be extracted.
+#'   + `"normal"` always returns `Inf`.
+#'   + `"model"` returns model-based degrees of freedom, i.e. the number of
+#'     (estimated) parameters.
+#'   + For mixed models, can also be `"ml1"` (or `"m-l-1"`, approximation of
+#'     degrees of freedom based on a "m-l-1" heuristic as suggested by _Elff et
+#'     al. 2019_) or `"between-within"` (or `"betwithin"`).
+#'   + For mixed models of class `merMod`, `type` can also be `"satterthwaite"`
+#'     or `"kenward-roger"` (or `"kenward"`). See 'Details'.
 #'
-#' For models with z-statistic, the returned degrees of freedom for model parameters
-#' is `Inf` (unless `method = "ml1"` or `method = "betwithin"`), because there is
-#' only one distribution for the related test statistic.
+#' Usually, when degrees of freedom are required to calculate p-values or
+#' confidence intervals, `type = "wald"` is likely to be the best choice in
+#' most cases.
+#' @param ... Currently not used.
 #'
 #' @note
 #' In many cases, `degrees_of_freedom()` returns the same as `df.residuals()`,
diff --git a/man/degrees_of_freedom.Rd b/man/degrees_of_freedom.Rd
index 4d403f67b..291bd55aa 100644
--- a/man/degrees_of_freedom.Rd
+++ b/man/degrees_of_freedom.Rd
@@ -12,45 +12,38 @@ dof(model, method = "analytical", ...)
 \arguments{
 \item{model}{A statistical model.}
 
-\item{method}{Can be \code{"analytical"} (default, DoFs are estimated based
-on the model type), \code{"residual"} in which case they are directly taken
-from the model if available (for Bayesian models, the goal (looking for
-help to make it happen) would be to refit the model as a frequentist one
-before extracting the DoFs), \code{"ml1"} (see \code{\link[=dof_ml1]{dof_ml1()}}), \code{"betwithin"}
-(see \code{\link[=dof_betwithin]{dof_betwithin()}}), \code{"satterthwaite"} (see \code{\link[=dof_satterthwaite]{dof_satterthwaite()}}),
-\code{"kenward"} (see \code{\link[=dof_kenward]{dof_kenward()}}) or \code{"any"}, which tries to extract DoF
-by any of those methods, whichever succeeds. See 'Details'.}
+\item{method}{Type of approximation for the degrees of freedom. Can be one of
+the following:
+\itemize{
+\item \code{"residual"} (aka \code{"analytical"}) returns the residual degrees of
+freedom, which usually is what \code{\link[stats:df.residual]{stats::df.residual()}} returns. If a
+model object has no method to extract residual degrees of freedom, these
+are calculated as \code{n-p}, i.e. the number of observations minus the number
+of estimated parameters. If residual degrees of freedom cannot be extracted
+by either approach, returns \code{Inf}.
+\item \code{"wald"} returns residual (aka analytical) degrees of freedom for models
+with t-statistic, \code{1} for models with Chi-squared statistic, and \code{Inf} for
+all other models. Also returns \code{Inf} if residual degrees of freedom cannot
+be extracted.
+\item \code{"normal"} always returns \code{Inf}.
+\item \code{"model"} returns model-based degrees of freedom, i.e. the number of
+(estimated) parameters.
+\item For mixed models, can also be \code{"ml1"} (or \code{"m-l-1"}, approximation of
+degrees of freedom based on a "m-l-1" heuristic as suggested by \emph{Elff et
+al. 2019}) or \code{"between-within"} (or \code{"betwithin"}).
+\item For mixed models of class \code{merMod}, \code{type} can also be \code{"satterthwaite"}
+or \code{"kenward-roger"} (or \code{"kenward"}). See 'Details'.
+}
+
+Usually, when degrees of freedom are required to calculate p-values or
+confidence intervals, \code{type = "wald"} is likely to be the best choice in
+most cases.}
 
 \item{...}{Currently not used.}
 }
 \description{
 Estimate or extract degrees of freedom of models parameters.
 }
-\details{
-Methods for calculating degrees of freedom:
-\itemize{
-\item \code{"analytical"} for models of class \code{lmerMod}, Kenward-Roger approximated
-degrees of freedoms are calculated, for other models, \code{n-k} (number of
-observations minus number of parameters).
-\item \code{"residual"} tries to extract residual degrees of freedom, and returns
-\code{Inf} if residual degrees of freedom could not be extracted.
-\item \code{"any"} first tries to extract residual degrees of freedom, and if these
-are not available, extracts analytical degrees of freedom.
-\item \code{"nokr"} same as \code{"analytical"}, but does not Kenward-Roger approximation
-for models of class \code{lmerMod}. Instead, always uses \code{n-k} to calculate df
-for any model.
-\item \code{"normal"} returns \code{Inf}.
-\item \code{"wald"} returns residual df for models with t-statistic, and \code{Inf} for all other models.
-\item \code{"kenward"} calls \code{\link[=dof_kenward]{dof_kenward()}}.
-\item \code{"satterthwaite"} calls \code{\link[=dof_satterthwaite]{dof_satterthwaite()}}.
-\item \code{"ml1"} calls \code{\link[=dof_ml1]{dof_ml1()}}.
-\item \code{"betwithin"} calls \code{\link[=dof_betwithin]{dof_betwithin()}}.
-}
-
-For models with z-statistic, the returned degrees of freedom for model parameters
-is \code{Inf} (unless \code{method = "ml1"} or \code{method = "betwithin"}), because there is
-only one distribution for the related test statistic.
-}
 \note{
 In many cases, \code{degrees_of_freedom()} returns the same as \code{df.residuals()},
 or \code{n-k} (number of observations minus number of parameters). However,