diff --git a/R/ctl_new_pillar.R b/R/ctl_new_pillar.R
index 3cda3a9f1..0bca0d8d4 100644
--- a/R/ctl_new_pillar.R
+++ b/R/ctl_new_pillar.R
@@ -1,31 +1,21 @@
-#' Customize your tibble subclass
+#' Customize the appearance of simple pillars in your tibble subclass
+#'
+#' @description
+#' `r lifecycle::badge("experimental")`
 #'
 #' Gain full control over the appearance of the pillars of your tibble subclass
 #' in its body.
-#' These methods are intended for implementers of subclasses of the `"tbl"`
-#' class.
+#' This method is intended for implementers of subclasses of the `"tbl"` class.
 #' Users will rarely need them.
 #'
+#' @details
 #' `ctl_new_pillar()` is called to construct pillars for regular (one-dimensional)
 #' vectors.
 #' The default implementation returns an object constructed with [pillar()].
-#' Extend this method to tweak pillar components returned from the default
+#' Extend this method to modify the pillar components returned from the default
 #' implementation.
 #' Override this method to completely change the appearance of the pillars.
-#'
-#' `ctl_new_pillar_list()` is called to construct a list of pillars.
-#' It also works for compound pillars: columns that are data frames, matrices or
-#' arrays.
-#' This method is also called to initiate the construction of all pillars
-#' in the tibble to be printed.
-#' If called for a regular one-dimensional vector, it returns a list of length
-#' one.
-#' In any case, all pillars in the returned list of pillars represent only the
-#' first column in case of compound columns.
-#' This ensures that only those pillars that are shown are constructed.
-#' To print all columns of a packed data frame, `ctl_new_pillar_list()`
-#' eventually calls itself recursively.
-#' Users will only rarely need to override this method if ever.
+#' Components are created with [new_pillar_component()] or [pillar_component()].
 #'
 #' All components must be of the same height.
 #' This restriction may be levied in the future.
@@ -35,12 +25,14 @@
 #'
 #' @inheritParams ellipsis::dots_empty
 #' @param controller The object of class `"tbl"` currently printed.
-#' @param x A vector, can also be a data frame, array or matrix.
-#'   in `ctl_new_pillar_list()`.
+#' @param x A simple (one-dimensional) vector.
 #' @param width The available width, can be a vector for multiple tiers.
-#'   If `NULL`, compute only the first pillar.
 #' @param title The title, derived from the name of the column in the data.
 #'
+#' @seealso
+#' See [ctl_new_pillar_list()] for creating pillar objects for compound columns:
+#' packed data frames, matrices, or arrays.
+#'
 #' @export
 #' @examplesIf rlang::is_installed("palmerpenguins") && requireNamespace("tibble")
 #' # Create pillar objects
@@ -49,25 +41,12 @@
 #'   palmerpenguins::penguins$species[1:3],
 #'   width = 60
 #' )
+#'
 #' ctl_new_pillar(
 #'   palmerpenguins::penguins,
 #'   palmerpenguins::penguins$bill_length_mm[1:3],
 #'   width = 60
 #' )
-#'
-#' # Packed data frame
-#' ctl_new_pillar_list(
-#'   tibble::tibble(),
-#'   palmerpenguins::penguins,
-#'   width = 60
-#' )
-#'
-#' # Packed matrix
-#' ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = 60)
-#'
-#' # Packed array
-#' ctl_new_pillar_list(tibble::tibble(), Titanic, width = 60)
-#'
 #' @examples
 #'
 #' # Customize output
@@ -116,45 +95,3 @@ max0 <- function(x) {
     0L
   }
 }
-
-#' @param first_pillar Can be passed to this method if the first pillar
-#'   for a compound pillar (or the pillar itself for a simple pillar)
-#'   has been computed already.
-#' @rdname ctl_new_pillar
-#' @export
-ctl_new_pillar_list <- function(controller, x, width, ..., title = NULL, first_pillar = NULL) {
-  "!!!!DEBUG ctl_new_pillar_list(`v(width)`, `v(title)`)"
-
-  check_dots_empty()
-
-  UseMethod("ctl_new_pillar_list")
-}
-
-#' @export
-ctl_new_pillar_list.tbl <- function(controller, x, width, ..., title = NULL, first_pillar = NULL) {
-  "!!!!DEBUG ctl_new_pillar_list.tbl(`v(width)`, `v(title)`)"
-
-  if (is.data.frame(x)) {
-    new_data_frame_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
-  } else if (is.matrix(x)) {
-    new_matrix_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
-  } else if (is.array(x) && length(dim(x)) > 1) {
-    new_array_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
-  } else {
-    if (is.null(first_pillar)) {
-      first_pillar <- ctl_new_pillar(controller, x, width, ..., title = prepare_title(title))
-    }
-    new_single_pillar_list(first_pillar, width)
-  }
-}
-
-prepare_title <- function(title) {
-  n_title <- length(title)
-  if (n_title == 0) {
-    title
-  } else if (grepl("^[[]", title[[n_title]])) {
-    paste0(paste(title[-n_title], collapse = "$"), title[[n_title]])
-  } else {
-    paste(title, collapse = "$")
-  }
-}
diff --git a/R/ctl_new_pillar_list.R b/R/ctl_new_pillar_list.R
index 18328262e..f94228d24 100644
--- a/R/ctl_new_pillar_list.R
+++ b/R/ctl_new_pillar_list.R
@@ -1,3 +1,111 @@
+#' Customize the appearance of compound pillars in your tibble subclass
+#'
+#' @description
+#' `r lifecycle::badge("experimental")`
+#'
+#' Gain full control over the appearance of the pillars of your tibble subclass
+#' in its body.
+#' This method is intended for implementers of subclasses of the `"tbl"` class.
+#' Users will rarely need them, and we also expect the default implementation
+#' to be sufficient for the vast majority of cases.
+#'
+#' @details
+#' `ctl_new_pillar_list()` is called to construct a list of pillars.
+#' If `x` is a regular (one-dimensional) vector, the list contains one pillar
+#' constructed by [ctl_new_pillar()].
+#' This method also works for compound columns: columns that are data frames,
+#' matrices or arrays, with the following behavior:
+#'
+#' - If `width` is `NULL`, the method always returns a list of length one
+#'   containing one pillar object that represents the first sub-column in this
+#'   compound column.
+#' - Otherwise, the returned list contains one pillar object for all sub-columns
+#'   that can be fit in the available horizontal space.
+#'   These pillar objects are obtained by calling `ctl_new_pillar_list()`
+#'   with `width = NULL` on each sub-column until the available width is
+#'   exhausted.
+#'
+#' This method is called to initiate the construction of all pillars
+#' in the tibble to be printed.
+#' To ensure that all packed columns that fit the available space are printed,
+#' `ctl_new_pillar_list()` may be called twice on the same input:
+#' once with `width = NULL`, and
+#' once with `width` corresponding to the then known available space
+#' and with `first_pillar` set to the pillar object constructed in the
+#' first call.
+#'
+#' @inheritParams ctl_new_pillar
+#' @param x A vector, can also be a data frame, matrix, or array.
+#' @param width The available width, can be a vector for multiple tiers.
+#'   If `NULL`, only the first pillar is instantiated.
+#' @param first_pillar Can be passed to this method if the first pillar
+#'   for a compound pillar (or the pillar itself for a simple pillar)
+#'   has been constructed already.
+#' @export
+#' @examplesIf rlang::is_installed("palmerpenguins") && requireNamespace("tibble")
+#' # Simple column
+#' ctl_new_pillar_list(
+#'   tibble::tibble(),
+#'   palmerpenguins::penguins$weight[1:3],
+#'   width = 10
+#' )
+#'
+#' # Packed data frame: unknown width
+#' ctl_new_pillar_list(
+#'   tibble::tibble(),
+#'   palmerpenguins::penguins[1:3, ],
+#'   width = NULL
+#' )
+#'
+#' # Packed data frame: known width
+#' ctl_new_pillar_list(
+#'   tibble::tibble(),
+#'   palmerpenguins::penguins,
+#'   width = 60
+#' )
+#'
+#' # Deeply packed data frame with known width:
+#' # showing only the first sub-column even if the width is sufficient
+#' ctl_new_pillar_list(
+#'   tibble::tibble(),
+#'   tibble::tibble(x = tibble::tibble(b = 1, c = 2), y = 3),
+#'   width = 60
+#' )
+#'
+#' # Packed matrix: unknown width
+#' ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = NULL)
+#'
+#' # Packed matrix: known width
+#' ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = 60)
+#'
+#' # Packed array
+#' ctl_new_pillar_list(tibble::tibble(), Titanic, width = 60)
+ctl_new_pillar_list <- function(controller, x, width, ..., title = NULL, first_pillar = NULL) {
+  "!!!!DEBUG ctl_new_pillar_list(`v(width)`, `v(title)`)"
+
+  check_dots_empty()
+
+  UseMethod("ctl_new_pillar_list")
+}
+
+#' @export
+ctl_new_pillar_list.tbl <- function(controller, x, width, ..., title = NULL, first_pillar = NULL) {
+  "!!!!DEBUG ctl_new_pillar_list.tbl(`v(width)`, `v(title)`)"
+
+  if (is.data.frame(x)) {
+    new_data_frame_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
+  } else if (is.matrix(x)) {
+    new_matrix_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
+  } else if (is.array(x) && length(dim(x)) > 1) {
+    new_array_pillar_list(x, controller, width, title = title, first_pillar = first_pillar)
+  } else {
+    if (is.null(first_pillar)) {
+      first_pillar <- ctl_new_pillar(controller, x, width, ..., title = prepare_title(title))
+    }
+    new_single_pillar_list(first_pillar, width)
+  }
+}
+
 new_data_frame_pillar_list <- function(x, controller, width, title, first_pillar = NULL) {
   "!!!!!DEBUG new_data_frame_pillar_list(`v(width)`, `v(title)`)"
 
@@ -209,3 +317,14 @@ new_pillar_list <- function(pillar_list, extra, remaining_width, simple = FALSE)
     simple = simple
   )
 }
+
+prepare_title <- function(title) {
+  n_title <- length(title)
+  if (n_title == 0) {
+    title
+  } else if (grepl("^[[]", title[[n_title]])) {
+    paste0(paste(title[-n_title], collapse = "$"), title[[n_title]])
+  } else {
+    paste(title, collapse = "$")
+  }
+}
diff --git a/_pkgdown.yml b/_pkgdown.yml
index 6a0473c93..ff820ba0c 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -11,6 +11,7 @@ reference:
       - tbl_format_body
       - tbl_format_footer
       - ctl_new_pillar
+      - ctl_new_pillar_list
       - tbl_sum
       - glimpse
       - format_glimpse
diff --git a/man/ctl_new_pillar.Rd b/man/ctl_new_pillar.Rd
index d2781502f..7458df7db 100644
--- a/man/ctl_new_pillar.Rd
+++ b/man/ctl_new_pillar.Rd
@@ -2,65 +2,37 @@
 % Please edit documentation in R/ctl_new_pillar.R
 \name{ctl_new_pillar}
 \alias{ctl_new_pillar}
-\alias{ctl_new_pillar_list}
-\title{Customize your tibble subclass}
+\title{Customize the appearance of simple pillars in your tibble subclass}
 \usage{
 ctl_new_pillar(controller, x, width, ..., title = NULL)
-
-ctl_new_pillar_list(
-  controller,
-  x,
-  width,
-  ...,
-  title = NULL,
-  first_pillar = NULL
-)
 }
 \arguments{
 \item{controller}{The object of class \code{"tbl"} currently printed.}
 
-\item{x}{A vector, can also be a data frame, array or matrix.
-in \code{ctl_new_pillar_list()}.}
+\item{x}{A simple (one-dimensional) vector.}
 
-\item{width}{The available width, can be a vector for multiple tiers.
-If \code{NULL}, compute only the first pillar.}
+\item{width}{The available width, can be a vector for multiple tiers.}
 
 \item{...}{These dots are for future extensions and must be empty.}
 
 \item{title}{The title, derived from the name of the column in the data.}
-
-\item{first_pillar}{Can be passed to this method if the first pillar
-for a compound pillar (or the pillar itself for a simple pillar)
-has been computed already.}
 }
 \description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}}
+
 Gain full control over the appearance of the pillars of your tibble subclass
 in its body.
-These methods are intended for implementers of subclasses of the \code{"tbl"}
-class.
+This method is intended for implementers of subclasses of the \code{"tbl"} class.
 Users will rarely need them.
 }
 \details{
 \code{ctl_new_pillar()} is called to construct pillars for regular (one-dimensional)
 vectors.
 The default implementation returns an object constructed with \code{\link[=pillar]{pillar()}}.
-Extend this method to tweak pillar components returned from the default
+Extend this method to modify the pillar components returned from the default
 implementation.
 Override this method to completely change the appearance of the pillars.
-
-\code{ctl_new_pillar_list()} is called to construct a list of pillars.
-It also works for compound pillars: columns that are data frames, matrices or
-arrays.
-This method is also called to initiate the construction of all pillars
-in the tibble to be printed.
-If called for a regular one-dimensional vector, it returns a list of length
-one.
-In any case, all pillars in the returned list of pillars represent only the
-first column in case of compound columns.
-This ensures that only those pillars that are shown are constructed.
-To print all columns of a packed data frame, \code{ctl_new_pillar_list()}
-eventually calls itself recursively.
-Users will only rarely need to override this method if ever.
+Components are created with \code{\link[=new_pillar_component]{new_pillar_component()}} or \code{\link[=pillar_component]{pillar_component()}}.
 
 All components must be of the same height.
 This restriction may be levied in the future.
@@ -76,24 +48,12 @@ ctl_new_pillar(
   palmerpenguins::penguins$species[1:3],
   width = 60
 )
+
 ctl_new_pillar(
   palmerpenguins::penguins,
   palmerpenguins::penguins$bill_length_mm[1:3],
   width = 60
 )
-
-# Packed data frame
-ctl_new_pillar_list(
-  tibble::tibble(),
-  palmerpenguins::penguins,
-  width = 60
-)
-
-# Packed matrix
-ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = 60)
-
-# Packed array
-ctl_new_pillar_list(tibble::tibble(), Titanic, width = 60)
 \dontshow{\}) # examplesIf}
 
 # Customize output
@@ -121,3 +81,7 @@ vctrs::new_data_frame(
   class = c("line_tbl", "tbl")
 )
 }
+\seealso{
+See \code{\link[=ctl_new_pillar_list]{ctl_new_pillar_list()}} for creating pillar objects for compound columns:
+packed data frames, matrices, or arrays.
+}
diff --git a/man/ctl_new_pillar_list.Rd b/man/ctl_new_pillar_list.Rd
new file mode 100644
index 000000000..e7464f088
--- /dev/null
+++ b/man/ctl_new_pillar_list.Rd
@@ -0,0 +1,107 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/ctl_new_pillar_list.R
+\name{ctl_new_pillar_list}
+\alias{ctl_new_pillar_list}
+\title{Customize the appearance of compound pillars in your tibble subclass}
+\usage{
+ctl_new_pillar_list(
+  controller,
+  x,
+  width,
+  ...,
+  title = NULL,
+  first_pillar = NULL
+)
+}
+\arguments{
+\item{controller}{The object of class \code{"tbl"} currently printed.}
+
+\item{x}{A vector, can also be a data frame, matrix, or array.}
+
+\item{width}{The available width, can be a vector for multiple tiers.
+If \code{NULL}, only the first pillar is instantiated.}
+
+\item{...}{These dots are for future extensions and must be empty.}
+
+\item{title}{The title, derived from the name of the column in the data.}
+
+\item{first_pillar}{Can be passed to this method if the first pillar
+for a compound pillar (or the pillar itself for a simple pillar)
+has been constructed already.}
+}
+\description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}}
+
+Gain full control over the appearance of the pillars of your tibble subclass
+in its body.
+This method is intended for implementers of subclasses of the \code{"tbl"} class.
+Users will rarely need them, and we also expect the default implementation
+to be sufficient for the vast majority of cases.
+}
+\details{
+\code{ctl_new_pillar_list()} is called to construct a list of pillars.
+If \code{x} is a regular (one-dimensional) vector, the list contains one pillar
+constructed by \code{\link[=ctl_new_pillar]{ctl_new_pillar()}}.
+This method also works for compound columns: columns that are data frames,
+matrices or arrays, with the following behavior:
+\itemize{
+\item If \code{width} is \code{NULL}, the method always returns a list of length one
+containing one pillar object that represents the first sub-column in this
+compound column.
+\item Otherwise, the returned list contains one pillar object for all sub-columns
+that can be fit in the available horizontal space.
+These pillar objects are obtained by calling \code{ctl_new_pillar_list()}
+with \code{width = NULL} on each sub-column until the available width is
+exhausted.
+}
+
+This method is called to initiate the construction of all pillars
+in the tibble to be printed.
+To ensure that all packed columns that fit the available space are printed,
+\code{ctl_new_pillar_list()} may be called twice on the same input:
+once with \code{width = NULL}, and
+once with \code{width} corresponding to the then known available space
+and with \code{first_pillar} set to the pillar object constructed in the
+first call.
+}
+\examples{
+\dontshow{if (rlang::is_installed("palmerpenguins") && requireNamespace("tibble")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
+# Simple column
+ctl_new_pillar_list(
+  tibble::tibble(),
+  palmerpenguins::penguins$weight[1:3],
+  width = 10
+)
+
+# Packed data frame: unknown width
+ctl_new_pillar_list(
+  tibble::tibble(),
+  palmerpenguins::penguins[1:3, ],
+  width = NULL
+)
+
+# Packed data frame: known width
+ctl_new_pillar_list(
+  tibble::tibble(),
+  palmerpenguins::penguins,
+  width = 60
+)
+
+# Deeply packed data frame with known width:
+# showing only the first sub-column even if the width is sufficient
+ctl_new_pillar_list(
+  tibble::tibble(),
+  tibble::tibble(x = tibble::tibble(b = 1, c = 2), y = 3),
+  width = 60
+)
+
+# Packed matrix: unknown width
+ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = NULL)
+
+# Packed matrix: known width
+ctl_new_pillar_list(tibble::tibble(), matrix(1:6, ncol = 2), width = 60)
+
+# Packed array
+ctl_new_pillar_list(tibble::tibble(), Titanic, width = 60)
+\dontshow{\}) # examplesIf}
+}