diff --git a/DESCRIPTION b/DESCRIPTION
index 71793e916..140445fc0 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Type: Package
 Package: performance
 Title: Assessment of Regression Models Performance
-Version: 0.12.0.1
+Version: 0.12.0.2
 Authors@R: 
     c(person(given = "Daniel",
              family = "Lüdecke",
diff --git a/NEWS.md b/NEWS.md
index 8ebbb8b3d..8aecc62b2 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -4,7 +4,12 @@
 
 * `icc()` and `r2_nakagawa()` get a `null_model` argument. This can be useful
   when computing R2 or ICC for mixed models, where the internal computation of
-  the null model fails.
+  the null model fails, or when you already have fit the null model and want
+  to save time.
+
+* `icc()` and `r2_nakagawa()` get a `approximation` argument indicating the 
+  approximation method for the distribution-specific (residual) variance. See
+  Nakagawa et al. 2017 for details.
 
 # performance 0.12.0
 
diff --git a/R/icc.R b/R/icc.R
index 27b945481..8fc19db13 100644
--- a/R/icc.R
+++ b/R/icc.R
@@ -34,9 +34,11 @@
 #' However, these intervals are rather inaccurate and often too narrow. It is
 #' recommended to calculate bootstrapped confidence intervals for mixed models.
 #' @param verbose Toggle warnings and messages.
-#' @param null_model Optional, a null model to compute the random effect variances.
-#' Should only be used if calculation of r-squared or ICC fails when `null_model`
-#' is not specified.
+#' @param null_model Optional, a null model to compute the random effect variances,
+#' which is passed to [`insight::get_variance()`]. Usually only required if
+#' calculation of r-squared or ICC fails when `null_model` is not specified. If
+#' calculating the null model takes longer and you already have fit the null
+#' model, you can pass it here, too, to speed up the process.
 #' @param ... Arguments passed down to `lme4::bootMer()` or `boot::boot()`
 #' for bootstrapped ICC or R2.
 #'
@@ -173,6 +175,7 @@ icc <- function(model,
                 iterations = 100,
                 ci_method = NULL,
                 null_model = NULL,
+                approximation = "lognormal",
                 verbose = TRUE,
                 ...) {
   # special handling for smicd::semLme()
@@ -201,7 +204,12 @@ icc <- function(model,
   }
 
   # calculate random effect variances
-  vars <- .compute_random_vars(model, tolerance, null_model = null_model)
+  vars <- .compute_random_vars(
+    model,
+    tolerance = tolerance,
+    null_model = null_model,
+    approximation = approximation
+  )
 
   # return if ICC couldn't be computed
   if (is.null(vars) || all(is.na(vars))) {
@@ -535,6 +543,7 @@ print.icc_decomposed <- function(x, digits = 2, ...) {
                                  name_fun = "icc()",
                                  name_full = "ICC",
                                  null_model = null_model,
+                                 approximation = "lognormal",
                                  verbose = TRUE) {
   vars <- tryCatch(
     insight::get_variance(model,
@@ -542,6 +551,7 @@ print.icc_decomposed <- function(x, digits = 2, ...) {
       name_full = name_full,
       tolerance = tolerance,
       null_model = null_model,
+      approximation = approximation,
       verbose = verbose
     ),
     error = function(e) {
diff --git a/R/r2_nakagawa.R b/R/r2_nakagawa.R
index cdd884e24..f65c23a5a 100644
--- a/R/r2_nakagawa.R
+++ b/R/r2_nakagawa.R
@@ -58,6 +58,7 @@ r2_nakagawa <- function(model,
                         iterations = 100,
                         ci_method = NULL,
                         null_model = NULL,
+                        approximation = "lognormal",
                         verbose = TRUE,
                         ...) {
   # calculate random effect variances
@@ -66,6 +67,7 @@ r2_nakagawa <- function(model,
     tolerance,
     components = c("var.fixed", "var.residual"),
     null_model = null_model,
+    approximation = approximation,
     name_fun = "r2()",
     name_full = "r-squared"
   )
diff --git a/man/icc.Rd b/man/icc.Rd
index 5f4110375..89ae6a9d0 100644
--- a/man/icc.Rd
+++ b/man/icc.Rd
@@ -13,6 +13,7 @@ icc(
   iterations = 100,
   ci_method = NULL,
   null_model = NULL,
+  approximation = "lognormal",
   verbose = TRUE,
   ...
 )
@@ -49,9 +50,15 @@ to calculate analytical confidence assuming a chi-squared distribution.
 However, these intervals are rather inaccurate and often too narrow. It is
 recommended to calculate bootstrapped confidence intervals for mixed models.}
 
-\item{null_model}{Optional, a null model to compute the random effect variances.
-Should only be used if calculation of r-squared or ICC fails when \code{null_model}
-is not specified.}
+\item{null_model}{Optional, a null model to compute the random effect variances,
+which is passed to \code{\link[insight:get_variance]{insight::get_variance()}}. Usually only required if
+calculation of r-squared or ICC fails when \code{null_model} is not specified. If
+calculating the null model takes longer and you already have fit the null
+model, you can pass it here, too, to speed up the process.}
+
+\item{approximation}{Character string, indicating the approximation method
+for the distribution-specific (residual) variance. Can be \code{"lognormal"}
+(default), \code{"delta"} or \code{"trigamma"}. See \emph{Nakagawa et al. 2017} for details.}
 
 \item{verbose}{Toggle warnings and messages.}
 
diff --git a/man/r2_nakagawa.Rd b/man/r2_nakagawa.Rd
index da1cbf00e..13d2d1e35 100644
--- a/man/r2_nakagawa.Rd
+++ b/man/r2_nakagawa.Rd
@@ -12,6 +12,7 @@ r2_nakagawa(
   iterations = 100,
   ci_method = NULL,
   null_model = NULL,
+  approximation = "lognormal",
   verbose = TRUE,
   ...
 )
@@ -48,9 +49,15 @@ to calculate analytical confidence assuming a chi-squared distribution.
 However, these intervals are rather inaccurate and often too narrow. It is
 recommended to calculate bootstrapped confidence intervals for mixed models.}
 
-\item{null_model}{Optional, a null model to compute the random effect variances.
-Should only be used if calculation of r-squared or ICC fails when \code{null_model}
-is not specified.}
+\item{null_model}{Optional, a null model to compute the random effect variances,
+which is passed to \code{\link[insight:get_variance]{insight::get_variance()}}. Usually only required if
+calculation of r-squared or ICC fails when \code{null_model} is not specified. If
+calculating the null model takes longer and you already have fit the null
+model, you can pass it here, too, to speed up the process.}
+
+\item{approximation}{Character string, indicating the approximation method
+for the distribution-specific (residual) variance. Can be \code{"lognormal"}
+(default), \code{"delta"} or \code{"trigamma"}. See \emph{Nakagawa et al. 2017} for details.}
 
 \item{verbose}{Toggle warnings and messages.}