diff --git a/NEWS.md b/NEWS.md
index 55853fc30..59a81ab58 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -8,6 +8,9 @@
   `component` argument gains the `"full"` option, to return the full
   variance-covariance matrix, including the random effects (theta parameters).
 
+* `format_p()` now also gets a `lead_zero` argument, to keep or drop the leading
+  zero of a formatted p-value.
+
 * `format_table()` now also formats ROPE columns for superiority and inferiority.
 
 * `format_table()` protects integer columns for non-specific column types.
diff --git a/R/format_p.R b/R/format_p.R
index 32803db77..57995b09f 100644
--- a/R/format_p.R
+++ b/R/format_p.R
@@ -17,6 +17,9 @@
 #'   If `"scientific"`, control the number of digits by adding the value as
 #'   a suffix, e.g.m `digits = "scientific4"` to have scientific notation
 #'   with 4 decimal places.
+#' @param lead_zero Logical, if `FALSE` (default), removes leading zero
+#'   before decimal separator. Otherwise, retain leading zero except when
+#'   p value is truncated
 #' @param ... Arguments from other methods.
 #' @inheritParams format_value
 #'
@@ -40,6 +43,7 @@ format_p <- function(p,
                      missing = "",
                      decimal_separator = NULL,
                      digits = 3,
+                     lead_zero = FALSE,
                      ...) {
   # only convert p if it's a valid numeric, or at least coercible to
   # valid numeric values...
@@ -59,6 +63,15 @@ format_p <- function(p,
     digits <- 3
   }
 
+  # hard-coded thresholds for small p-values, including or excluding leading zero
+  if (lead_zero) {
+    low_p <- "< 0.001***"
+    high_p <- "> 0.999"
+  } else {
+    low_p <- "< .001***"
+    high_p <- "> .999"
+  }
+
   if (is.character(digits) && grepl("scientific", digits, fixed = TRUE)) {
     digits <- tryCatch(as.numeric(gsub("scientific", "", digits, fixed = TRUE)),
       error = function(e) NA
@@ -79,11 +92,11 @@ format_p <- function(p,
     )
   } else if (digits <= 3) {
     p_text <- ifelse(is.na(p), NA,
-      ifelse(p < 0.001, "< .001***", # nolint
-        ifelse(p < 0.01, paste0("= ", format_value(p, digits), "**"), # nolint
-          ifelse(p < 0.05, paste0("= ", format_value(p, digits), "*"), # nolint
-            ifelse(p > 0.999, "> .999", # nolint
-              paste0("= ", format_value(p, digits))
+      ifelse(p < 0.001, low_p, # nolint
+        ifelse(p < 0.01, paste0("= ", format_value(p, digits, lead_zero = lead_zero), "**"), # nolint
+          ifelse(p < 0.05, paste0("= ", format_value(p, digits, lead_zero = lead_zero), "*"), # nolint
+            ifelse(p > 0.999, high_p, # nolint
+              paste0("= ", format_value(p, digits, lead_zero = lead_zero))
             )
           )
         )
@@ -91,10 +104,10 @@ format_p <- function(p,
     )
   } else {
     p_text <- ifelse(is.na(p), NA,
-      ifelse(p < 0.001, paste0("= ", format_value(p, digits), "***"), # nolint
-        ifelse(p < 0.01, paste0("= ", format_value(p, digits), "**"), # nolint
-          ifelse(p < 0.05, paste0("= ", format_value(p, digits), "*"), # nolint
-            paste0("= ", format_value(p, digits))
+      ifelse(p < 0.001, paste0("= ", format_value(p, digits, lead_zero = lead_zero), "***"), # nolint
+        ifelse(p < 0.01, paste0("= ", format_value(p, digits, lead_zero = lead_zero), "**"), # nolint
+          ifelse(p < 0.05, paste0("= ", format_value(p, digits, lead_zero = lead_zero), "*"), # nolint
+            paste0("= ", format_value(p, digits, lead_zero = lead_zero))
           )
         )
       )
diff --git a/man/format_p.Rd b/man/format_p.Rd
index 25e030e9e..6412043da 100644
--- a/man/format_p.Rd
+++ b/man/format_p.Rd
@@ -13,6 +13,7 @@ format_p(
   missing = "",
   decimal_separator = NULL,
   digits = 3,
+  lead_zero = FALSE,
   ...
 )
 }
@@ -42,6 +43,10 @@ If \code{"scientific"}, control the number of digits by adding the value as
 a suffix, e.g.m \code{digits = "scientific4"} to have scientific notation
 with 4 decimal places.}
 
+\item{lead_zero}{Logical, if \code{FALSE} (default), removes leading zero
+before decimal separator. Otherwise, retain leading zero except when
+p value is truncated}
+
 \item{...}{Arguments from other methods.}
 }
 \value{
diff --git a/tests/testthat/test-format.R b/tests/testthat/test-format.R
index ab6c6b717..e727355ce 100644
--- a/tests/testthat/test-format.R
+++ b/tests/testthat/test-format.R
@@ -143,6 +143,17 @@ test_that("format_p", {
   expect_identical(nchar(format_p(0.02)), 9L)
   expect_identical(nchar(format_p(0.02, stars = TRUE)), 10L)
   expect_identical(nchar(format_p(0.02, stars_only = TRUE)), 1L)
+
+  expect_identical(format_p(0.02), "p = .020")
+  expect_identical(format_p(0.02, lead_zero = TRUE), "p = 0.020")
+  expect_identical(format_p(0.02, stars = TRUE), "p = .020*")
+  expect_identical(format_p(0.02, stars = TRUE, lead_zero = TRUE), "p = 0.020*")
+  expect_identical(format_p(0.0214568, digits = "apa"), "p = .021")
+  expect_identical(format_p(0.0214568, digits = "apa", lead_zero = TRUE), "p = 0.021")
+  expect_identical(format_p(0.00003, digits = "apa"), "p < .001")
+  expect_identical(format_p(0.00003, digits = "apa", lead_zero = TRUE), "p < 0.001")
+  expect_identical(format_p(0.00003, digits = 5), "p = .00003")
+  expect_identical(format_p(0.00003, digits = 5, lead_zero = TRUE), "p = 0.00003")
 })
 
 test_that("format_table, other CI columns", {