diff --git a/R/find_k.R b/R/find_k.R
index c58a287..aeb0542 100644
--- a/R/find_k.R
+++ b/R/find_k.R
@@ -8,13 +8,15 @@
 #' @param n integer; number of observations. Ignored if \code{variables} is provided.
 #' @param p integer; number of variables to factor analyze. Ignored if\code{variables} is provided.
 #' @param m integer; maximum number of factors expected to be extracted from \code{variables}. Default is \code{p} / 4 (i.e., 4 variables per factor).
+#' @param est.pars integer; number estimated model parameters. Default is 2\code{p}  + \code{m}(\code{m} - 1)/2, which reflects a standardized model with simple structure (e.g., no cross-loadings, higher order factors) or constraints (e.g., tau-equivalence)
 #' @param max.k integer; maximum number of folds. Default is 10. \code{NULL} indicates no maximum.
-#' @param min.n integer; minimum sample size per fold. Default is 200 based on simulations from Curran et al. (2003).
+#' @param min.nk integer; minimum sample size per fold. Default is 200 based on simulations from Curran et al. (2003).
 #' @param rmsea0 numeric; RMSEA under the null hypothesis.
 #' @param rmseaA numeric; RMSEA under the alternative hypothesis.
 #' @param ... other arguments passed to \code{\link[semTools]{findRMSEAsamplesize}}.
 #'
-#' @return named vector with the number of folds (k), sample size suggested by the power analysis (power.n), and the actual sample size used for determining k (actual.n).
+#' @return named vector with the number of folds (k), sample size suggested for each fold by the power analysis (power.nk),
+#' the degrees of freedom used for power analysis, and the sample size for each fold used for determining k (nk)--the higher of \code{power.nk} and \code{min.nk}.
 #'
 #' @references
 #' Curran, P. J., Bollen, K. A., Chen, F., Paxton, P., & Kirby, J. B. (2003). Finite sampling properties of the point estimates and confidence intervals of the RMSEA. *Sociological Methods & Research, 32*(2), 208-252. \doi{10.1177/0049124103256130}
@@ -22,16 +24,19 @@
 #' MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. *Psychological Methods, 1*(2), 130–149. \doi{10.1037/1082-989X.1.2.130}
 #'
 #' @examples
-#' find_k(n = 900, p = 20, m = 3)
+#' find_k(n = 900, p = 11, m = 3)
 #'
 #' # adjust precision
-#' find_k(n = 900, p = 20, m = 3, rmsea0 = .03, rmseaA = .10)
+#' find_k(n = 900, p = 11, m = 3, rmsea0 = .03, rmseaA = .10)
+#'
+#' # adjust number of estimated parameters (e.g., constrain all factor loadings to be equal)
+#' find_k(n = 900, p = 11, m = 3, est.pars = 15)
 #'
 #' @importFrom semTools findRMSEAsamplesize
 #' @export
 #' @md
 
-find_k <- function(variables, n, p, m = NULL, max.k = 10, min.n = 200,
+find_k <- function(variables, n, p, m = NULL, est.pars = NULL, max.k = 10, min.nk = 200,
                   rmsea0 = .05, rmseaA = .08, ...){
 
   if(!missing(variables)){
@@ -44,14 +49,18 @@ find_k <- function(variables, n, p, m = NULL, max.k = 10, min.n = 200,
     m <- floor(p / 4)
   }
 
-  df <- p*(p+1)/2 - (2*p + (m*(m-1))/2)  # information from cov - (loadings & residuals + factor covs [w/ factor vars = 1])
-  power.n <- semTools::findRMSEAsamplesize(rmsea0 = rmsea0, rmseaA = rmseaA, df = df, ...)
+  if(is.null(est.pars)){
+    est.pars <- 2*p + m*(m-1)/2  # assumes standardized model identification [factor vars = 1] and no constraints
+  }
+  # information from cov - estimated parameters
+  df <- p*(p+1)/2 - est.pars
+  power.nk <- semTools::findRMSEAsamplesize(rmsea0 = rmsea0, rmseaA = rmseaA, df = df, ...)
   # returns sample size
   # defaults are power = .8, alpha = .05, and group = 1 unless changed via ...
 
-  actual.n <- ifelse(power.n < min.n, min.n, power.n)
+  nk <- ifelse(power.nk < min.nk, min.nk, power.nk)
 
-  k <- floor(n / actual.n)
+  k <- floor(n / nk)
   if(k < 2){
     message("Power analysis indicates the sample size is too small for k-fold cross validation.
     Adjust assumptions or manually create a single holdout sample.")
@@ -60,6 +69,6 @@ find_k <- function(variables, n, p, m = NULL, max.k = 10, min.n = 200,
   k <- ifelse(k > max.k, max.k, k)
   }
 
-  return(c(k = k, power.n = power.n, actual.n = actual.n))
+  return(c(k = k, power.nk = power.nk, df = df, nk = nk))
 }
 
diff --git a/man/find_k.Rd b/man/find_k.Rd
index 959e91c..7b8da47 100644
--- a/man/find_k.Rd
+++ b/man/find_k.Rd
@@ -9,8 +9,9 @@ find_k(
   n,
   p,
   m = NULL,
+  est.pars = NULL,
   max.k = 10,
-  min.n = 200,
+  min.nk = 200,
   rmsea0 = 0.05,
   rmseaA = 0.08,
   ...
@@ -26,9 +27,11 @@ The power analysis assumes all observations have complete data. Use \code{n} arg
 
 \item{m}{integer; maximum number of factors expected to be extracted from \code{variables}. Default is \code{p} / 4 (i.e., 4 variables per factor).}
 
+\item{est.pars}{integer; number estimated model parameters. Default is 2\code{p}  + \code{m}(\code{m} - 1)/2, which reflects a standardized model with simple structure (e.g., no cross-loadings, higher order factors) or constraints (e.g., tau-equivalence)}
+
 \item{max.k}{integer; maximum number of folds. Default is 10. \code{NULL} indicates no maximum.}
 
-\item{min.n}{integer; minimum sample size per fold. Default is 200 based on simulations from Curran et al. (2003).}
+\item{min.nk}{integer; minimum sample size per fold. Default is 200 based on simulations from Curran et al. (2003).}
 
 \item{rmsea0}{numeric; RMSEA under the null hypothesis.}
 
@@ -37,17 +40,21 @@ The power analysis assumes all observations have complete data. Use \code{n} arg
 \item{...}{other arguments passed to \code{\link[semTools]{findRMSEAsamplesize}}.}
 }
 \value{
-named vector with the number of folds (k), sample size suggested by the power analysis (power.n), and the actual sample size used for determining k (actual.n).
+named vector with the number of folds (k), sample size suggested for each fold by the power analysis (power.nk),
+the degrees of freedom used for power analysis, and the sample size for each fold used for determining k (nk)--the higher of \code{power.nk} and \code{min.nk}.
 }
 \description{
 This function is specifically for determining \emph{k} in the context of factor analysis using
 change in RMSEA as the criterion for identifying the optimal factor model.
 }
 \examples{
-find_k(n = 900, p = 20, m = 3)
+find_k(n = 900, p = 11, m = 3)
 
 # adjust precision
-find_k(n = 900, p = 20, m = 3, rmsea0 = .03, rmseaA = .10)
+find_k(n = 900, p = 11, m = 3, rmsea0 = .03, rmseaA = .10)
+
+# adjust number of estimated parameters (e.g., constrain all factor loadings to be equal)
+find_k(n = 900, p = 11, m = 3, est.pars = 15)
 
 }
 \references{